Best elementary algebra books according to redditors
We found 266 Reddit comments discussing the best elementary algebra books. We ranked the 96 resulting products by number of redditors who mentioned them. Here are the top 20.
We found 266 Reddit comments discussing the best elementary algebra books. We ranked the 96 resulting products by number of redditors who mentioned them. Here are the top 20.
Download this book illegally: https://www.amazon.com/Calculus-James-Stewart/dp/1285740629
This is the book currently used in top-tier high schools to learn calculus. It is highly accessible. It creates a spark, at least in me, that made me take that book to bed and learn so much all night.
You'll get lots of practice if you do their practice problems (especially the more complex and involved ones later). Calc 3 is also covered in this book.
Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.
Amazon search for Dover Books on mathematics
There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Pre-Calculus / Problem-Solving
Calculus
Linear Algebra
Differential Equations
Number Theory
Proof-Writing
Analysis
Complex Analysis
Functional Analysis
Partial Differential Equations
Higher-dimensional Calculus and Differential Geometry
Abstract Algebra
Geometry
Topology
Set Theory and Logic
Combinatorics / Discrete Math
Graph Theory
P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
Elementary Algebra For College Students (9th Edition)
Hardcover – January 3, 2014
Buy New Price: $193.79
http://www.amazon.com/gp/product/0321868064/ref=pd_lpo_sbs_dp_ss_1?pf_rd_p=1535523722&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0321620933&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=00BXKVJE4J820GBXED7Z
Elementary Algebra for College Students (8th Edition)
Hardcover – January 13, 2010
Buy New Price: $160.98
http://www.amazon.com/Elementary-Algebra-College-Students-8th/dp/0321620933/ref=sr_1_6?s=books&ie=UTF8&qid=1409444421&sr=1-6
This is multi-variable calculus. Any calculus book worth its weight will cover this.
You added an extra zero there.
This is what Americans use. It costs about as much as a used smart phone and it's way less powerful.
This is my calc text. With tax it comes to over $300.
Americans are dumb as fuck because we can't afford to learn =***(
I had to deal with the no internet thing for some time.
Find some place with free wi-fi(you are using phone?).
Download ebook/pdf reader, FBreader + PDF plugin is good (Assuming that you are using Android phone).
Install Firefox and this add-on Save Page WE, it also work for phones (tested with Android).
Then you can save pages from some of these web sites or Wikipedia:
Poor man's library:
http://gen.lib.rus.ec/
http://b-ok.org/
https://archive.org/
Some books:
[Harold Jacobs - Elementary Algebra] (https://www.amazon.com/Elementary-Algebra-Harold-R-Jacobs/dp/0716710471) (that's the most friendly and still not bullshit introduction I was able to find)
[Basic Mathematics by Serge Lang] (https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877) - Make sure that you understand the first 100-150 pages from the first book if you want to start this one.
Precalculus by David Cohen - Lang's Basic Mathematics is harder (and much more interesting) than this...
Use the three web sites written above to download them. PDF for better performance (and some times quality) on cheap phone, epub/djvu for the smaller size.
I think that free wi-fi will be easy to find. Reading books wouldn't be like watching videos but you will actually learn more. Compass, straightedge and protractor would be really useful.
I have a B.S. in mathematics, statistics emphasis - and am currently in the second semester of Linear Models in a M.S. Statistics program.
Contrary to popular opinion, I don't think Linear Algebra Done Right is suitable for learning linear algebra. Statistics - as far as I've gathered - is more focused on what is called "numerical linear algebra," rather than the more algebraic (and more abstract) approach that Axler takes.
It took a lot of research on my part to find better books. I personally believe that these resources are much better for covering the linear algebra needed for linear models (I recommend these after a first-course treatment in linear algebra):
I have also heard that Matrix Algebra Useful for Statistics by Searle is good, but I haven't read it yet.
If you feel like your linear algebra is particularly strong (i.e., you're comfortable with vector spaces, matrix operations, eigenvalues), you could try diving right into linear models. My personal favorite is Plane Answers to Complex Questions by Christensen. I reviewed this book on Amazon:
>It's a decent text. If you want to understand any part of this text, you need to have at least a first course in linear algebra covering matrices and vector spaces, some probability, and some "mathematical maturity."
>READ THE APPENDICES before you read any part of this text. READ THE APPENDICES. Take good notes on them and learn the appendices well. Then proceed to Chapter 1.
>Definitely one of the most readable books I've read, but it does take a long time to digest everything. If you don't have a teacher to take you through this material and you're completely new to it, you will find that some details are omitted, but these details aren't complicated enough that someone with an undergraduate degree in math wouldn't be able to figure them out.
>Highly recommended. The only thing I don't like about this text is some of its notation. It uses Cov(A) to mean the variance-covariance matrix of a random vector A, and Cov(A, B) to mean E[(A-E[A])(B-E[B])^transpose ]. I prefer using Var(A) for the former case. Furthermore, it uses ' instead of T to denote the transpose of a matrix.
No linear models text will cover all of the linear algebra used, however. If you get a linear models text, you should get your hands on one of the above linear algebra texts as well.
If you need a first course's treatment in Linear Algebra, I prefer [Linear Algebra and Its Applications](http://www.amazon.com/Linear-Algebra-Its-Applications-Edition/dp/0201709708) by Lay. The 3rd edition will suffice, although I think it's in the 5th edition now. Larson's [Elementary Linear Algebra*](http://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/1133110878/ref=sr_1_1?s=books&ie=UTF8&qid=1458047961&sr=1-1&keywords=larson+linear+algebra) is also a decent text; older editions are likely cheaper, but will likely give you a similar treatment as well, so you may want to look into these too. I learned from the 6th edition in my undergrad.
/u/another_user_name posted this list a while back. Actual aerospace textbooks are towards the bottom but you'll need a working knowledge of the prereqs first.
Non-core/Pre-reqs:
Mathematics:
Calculus.
1-4) Calculus, Stewart -- This is a very common book and I felt it was ok, but there's mixed opinions about it. Try to get a cheap, used copy.
1-4) Calculus, A New Horizon, Anton -- This is highly valued by many people, but I haven't read it.
1-4) Essential Calculus With Applications, Silverman -- Dover book.
More discussion in this reddit thread.
Linear Algebra
3) Linear Algebra and Its Applications,Lay -- I had this one in school. I think it was decent.
3) Linear Algebra, Shilov -- Dover book.
Differential Equations
4) An Introduction to Ordinary Differential Equations, Coddington -- Dover book, highly reviewed on Amazon.
G) Partial Differential Equations, Evans
G) Partial Differential Equations For Scientists and Engineers, Farlow
More discussion here.
Numerical Analysis
5) Numerical Analysis, Burden and Faires
Chemistry:
Physics:
2-4) Physics, Cutnel -- This was highly recommended, but I've not read it.
Programming:
Introductory Programming
Programming is becoming unavoidable as an engineering skill. I think Python is a strong introductory language that's got a lot of uses in industry.
Core Curriculum:
Introduction:
Aerodynamics:
Thermodynamics, Heat transfer and Propulsion:
Flight Mechanics, Stability and Control
5+) Flight Stability and Automatic Control, Nelson
5+)[Performance, Stability, Dynamics, and Control of Airplanes, Second Edition](http://www.amazon.com/Performance-Stability-Dynamics-Airplanes-Education/dp/1563475839/ref=sr_1_1?ie=UTF8&qid=1315534435&sr=8-1, Pamadi) -- I gather this is better than Nelson
Engineering Mechanics and Structures:
3-4) Engineering Mechanics: Statics and Dynamics, Hibbeler
6-8) Analysis and Design of Flight Vehicle Structures, Bruhn -- A good reference, never really used it as a text.
G) Introduction to the Mechanics of a Continuous Medium, Malvern
G) Fracture Mechanics, Anderson
G) Mechanics of Composite Materials, Jones
Electrical Engineering
Design and Optimization
Space Systems
Learning Calculus prior would be helpful, but probably not necessary. I'd recommend getting a Linear Algebra book and start working through it. I used this one in my university Linear Algebra course and it is fairly well written, and approachable. You can probably find this book online as a pdf somewhere.
Basic Algebra by Nathan Jacobson
Advanced Calculus by Shlomo Zvi Sternberg, Lynn Harold Loomis
Damn, son. That's way bigger than my guesstimate.
The amazon prices I checked out pinned the collection closer to $400, which granted is still really, really impressive.
In case you're curious this was my textbook. It's come down by a lot in price over a couple years. Brand new it was $365 in the shrink wrap from my school's store!
Eh, either way I'm wrong, just by a different amount.
E-books are poorly discounted (if at all,) cannot be bought used, and cannot be sold to recover some of the purchase cost. Is it any wonder students prefer paper?
Picking a Calculus book at random. Which would be more appealing to a cash starved student. Spending $208 or spending $167 with a strongly likely hood of reselling for ~$60 after fees. In this case paper is potentially half the cost of an e-book.
I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.
If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.
Basics
I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.
Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.
From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.
This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.
Intermediate
At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.
This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.
Advanced
Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.
Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.
Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.
Attention Publishers
This is why readers hate you. Note the version number. Seventh Edition? Really, how much has calculus changed in the past 20 years? The past 50? Or 100? I only graduated 4 years ago, and this is the second time they've cranked out a new version of the book since my freshman year.
Of course they quit printing the older editions, because they can cripple the market for used textbooks and force everyone to buy new versions. So they go and re-hash and reword a chapter here and there and pretend it's a "new" book somehow.
I seriously doubt it takes until the 4th, 5th, or 6th printing of a book for the publisher to recoup their investment; if it does, I think the only reason is that they're writing themselves such large checks.
This is good for many books. There are two types of textbooks:
An Introduction to Modern Astrophysics is an excellent and easy to read book:
https://www.amazon.com/dp/1108422160/ref=cm_sw_r_cp_apa_omrWBbDYB9MN3
It's commonly used for introductory Astrophysics courses. If you don't have a basic understanding of Calculus it won't make much sense so, if you really want to properly understand the subject, first study basic Calculus. A good introductory Calculus book would be this one:
https://www.amazon.com/dp/1285740629/ref=cm_sw_r_cp_apa_JdsWBbH1KXPAN.
You're also going to want a basic understanding of Physics so one more for that:
University Physics with Modern Physics (14th Edition)
https://www.amazon.com/dp/0321973615/ref=cm_sw_r_cp_apa_LfsWBbHJ83MT6
Those three books together should give you a basic understanding of Astrophysics and put your feet solidly on the road to further understanding. Read the Calculus book first (at least the first half of it or so) and then the Physics book. Then you'll be ready to dive into Carroll and Ostlie's book!
If you don't want to go quite that deep and you just want a really basic overview of the subject, you might consider finding Hawking's "A Briefer History of Time" or watching the PBS SpaceTime series in YouTube.
Edit: If the Calculus book is still a little unclear, your issue probably lies in Algebra. In that case, read this book before any of the others:
College Algebra (10th Edition)
https://www.amazon.com/dp/0321979478/ref=cm_sw_r_cp_apa_MqsWBbR985C30
Good luck on your journey! Give yourself at least a year or two to get through all of them and don't forget to work the problems!
Oh - download Kerbal Space Program and play it for a while. Trust me on this; you'll develop a second sense of basic orbital mechanics ;)
There is no guaranteed was to factor any arbitrary polynomial, sadly. You could look into synthetic division, which is probably the fastest general way to test possible roots of an arbitrary polynomial.
You're never going to escape the "if x is not zero" stuff because 0 really is different than every other number. 0x = y has no solutions for y =/= 0, whereas ax = y does for every a =/= 0. This sort of "we need to exclude this one silly case" thing shows up all over math. For any non-zero number... for any non-empty set... for any non-trivial solution...
In math you always look at the cases where n=1, n=2 first (whatever n is... in your case linear and quadratic functions). Starting with the easy case isn't bad... but losing sight of the harder cases or not learning how to deal with them at all is.
I learned elementary algebra from this book and this one, in that order, and I think they were both excellent at providing the sort of perspective on problems that you were looking for. I don't think that "buy an extra set of textbooks to read in your free time" was the solution you were looking for... but maybe.
The really fundamental rule of algebra is "do to one side what you do to the other", although in practice I usually picture moving terms from one side to the other (flipping the sign) when the thing that I'm doing to both sides is addition or subtraction. The other fundamental rule (haha there are two) is that you can replace any term with something that is equal to it. The third fundamental rule is to check your answer at the end to avoid spurious solutions you got because you took the wrong root or divided by zero or something. If what you have solves the equation, it's a correct answer, even if everything leading up to it was wrong. (It might not get full credit of course...)
Really, with elementary algebra, you will eventually find it to be completely intuitive if you stay in math/science... just by using it so often. If your class isn't giving you a good perspective on the subject, you can at least rest assured that that perspective will come with time. I totally understand your frustration, though. (For what it's worth, I really struggled in high school algebra I (not II for some reason). I eventually just got past that with lots of practice.)
I enjoyed the class. The professor was awesome, so that helped. I thought it was pretty easy, but I think that was because I had already been introduced to proofs. We did some Number Theory, Set Theory, Counting, Relations, Modular Arithmetic, Functions, Limits, Axiom of Choice and the Cantor-Schroder-Bernstein Theorem. We spent roughly two weeks on each subject, so we didn't go too in depth. At the end, we did some combinatorics because the professor likes combinatorics.
The book we used was A Transition to Advanced Mathematics by Douglas Smith. I didn't really use it at all. Our notes were sufficient.
I definitely think introduction to proof classes are helpful (and fun), but I would rather the school recommend a book to read over the summer so there is more room for another math elective. Naturally, this depends on the motivation of the school's students. My school has a bunch of lazy blobs. I doubt more than 5 would read a book over the summer.
tl;dr: you need to learn proofs to read most math books, but if nothing else there's a book at the bottom of this post that you can probably dive into with nothing beyond basic calculus skills.
Are you proficient in reading and writing proofs?
If you aren't, this is the single biggest skill that you need to learn (and, strangely, a skill that gets almost no attention in school unless you seek it out as an undergraduate). There are books devoted to developing this skill—How to Prove It is one.
After you've learned about proof (or while you're still learning about it), you can cut your teeth on some basic real analysis. Basic Elements of Real Analysis by Protter is a book that I'm familiar with, but there are tons of others. Ask around.
You don't have to start with analysis; you could start with algebra (Algebra and Geometry by Beardon is a nice little book I stumbled upon) or discrete (sorry, don't know any books to recommend), or something else. Topology probably requires at least a little familiarity with analysis, though.
The other thing to realize is that math books at upper-level undergraduate and beyond are usually terse and leave a lot to the reader (Rudin is famous for this). You should expect to have to sit down with pencil and paper and fill in gaps in explanations and proofs in order to keep up. This is in contrast to high-school/freshman/sophomore-style books like Stewart's Calculus where everything is spelled out on glossy pages with color pictures (and where proofs are mostly absent).
And just because: Visual Complex Analysis is a really great book. Complex numbers, functions and calculus with complex numbers, connections to geometry, non-Euclidean geometry, and more. Lots of explanation, and you don't really need to know how to do proofs.
If you're currently at the pre-calc level, you could probably get away with learning from khan academy for a little while. After that (and building some familiarity with proof writing), you'd be ready for some of the pure math classes like abstract algebra and real analysis. For those courses, you'll probably want to check out some Open Courseware. You'd want to treat it like a real class; watch the lectures online and read from the textbooks, while working on problem sets.
While you're working your way through the khan academy stuff, you might want to check out Stewart's calculus book; it's pretty solid for making your way through the calculus sequence.
I'd ask around for a good linear algebra book, since I haven't encountered a decent one that's at that level.
I’m not sure Khan Academy is the most useful source; most of the assigned exercises I looked at a few years ago seemed pretty much trivial. You just watch someone solve a problem on a video, and then do exactly the same steps but with slightly different details. It’s an exercise in memory and copying, not in thinking for yourself. Basically the same curriculum as standard high school courses, just at your own pace. See Lockhart, “A Mathematician’s Lament” and Toom, “Word Problems in Russia and America”.
If you are self-studying the Gelfand and Kisilev books /u/TheBloodyNine1 mentioned are nice Russian books with some good problems in them, but also some text. If the text exposition is too fast or high level you could try reading the algebra and geometry books by Harold Jacobs. These have easier (standard American style) exercises but gentler exposition. If you are looking for medium to hard (by typical American standards) problems but also a good amount of step-by-step help with solving them, you might enjoy the Art of Problem Solving books, including those about algebra, geometry, basic number theory, “precalculus”.
Or for something a bit more poetic, check out Lockhart’s book Measurement.
The best way to learn the “why” of things in a real way is by doing the work for yourself. If someone just tries to tell you it won’t really sink in – you have to struggle with something for yourself before the explanation even has any relevance. Sometimes a book of nothing but problems can be just as useful as a book full of text.
See if you can work your way through problems such as those in Mathematical Circles (Russian Experience) (designed for ambitious Russian middle school students). Or you can look at the problems used at Exeter (famous private high school): Math 1, Math 2, Math 3–4, Math 4–5, Math 6, Discrete Math.
Or see if you can solve some past contest math problems. E.g. pick up a copy of a past AMC 12 (or AMC 10 or AMC 8 if those are too hard), and see how many problems you can do if you let yourself try to solve each one for 20 minutes without looking up the answer.
If you get through some of those and want less typical fare there are some fun topics in A Decade of the Berkeley Math Circle.
For some more general advice about problem solving methods (alongside problems), the book Thinking Mathematically is nice.
To be honest, the fastest way to improve is to find an expert tutor/mentor/coach to meet with face to face. Self-studying from books or websites or learning from class lectures and completely independent work is much more difficult / less efficient. There might be free tutoring resources available in your area if you hunt around (e.g. sometimes colleges will do free tutoring for nearby high school students).
Finally, if you get stuck on anything (problem, topic, ...) in particular, try /r/learnmath.
Elementary Linear Algebra by Larson, Edwards and Falvo.
Amazon link here.
For Calculus:
Calculus Early Transcendentals by James Stewart
^ Link to Amazon
Khan Academy Calculus Youtube Playlist
For Physics:
Introductory Physics by Giancoli
^ Link to Amazon
Crash Course Physics Youtube Playlist
Here are additional reading materials when you're a bit farther along:
Mathematical Methods in the Physical Sciences by Mary Boas
Modern Physics by Randy Harris
Classical Mechanics by John Taylor
Introduction to Electrodynamics by Griffiths
Introduction to Quantum Mechanics by Griffiths
Introduction to Particle Physics by Griffiths
The Feynman Lectures
With most of these you will be able to find PDFs of the book and the solutions. Otherwise if you prefer hardcopies you can get them on Amazon. I used to be adigital guy but have switched to physical copies because they are easier to reference in my opinion. Let me know if this helps and if you need more.
Any introductory abstract algebra book will have the basics of of rings, ideals, and quotient rings, as well as a few other things.
My class on intro to group theory used Gallian's Contemporary Abstract Algebra, which I'm a pretty big fan of as an introduction. It's gentle and doesn't rush into things, but has a large amount of exercises, some of which will really stretch your understanding.
If you want something a little harder, but a little deeper, Artin's Algebra is very popular, and for very good reason. It'll help you develop your group theory knowledge as well.
This is the book I’m using right now in my first proofs class it’s pretty good at explaining the thought processes as well as it can be paired with How to Prove It by Daniel J. Velleman for a more through brake down of them problem types.
Get a good, straight-forward book. $12.92 +shipping, you cannot beat that.
Once you have your book, take it to the library with a calculator and a notebook, find one of their economy-sized sensory deprivation chambers that contain nothing but a desk and a florescent light, and just work through problems until your brain is fried. Do this every day. You learn math by using it, not by watching other people use it.
After that get a better book and do the same thing. Repeat as necessary. Use Khan Academy for when you get stuck, not to learn new ideas. Anybody can sit down and watch 20 hours of videos on the internet (well, not anybody... I can't, I get too distracted on the computer), but you're not going to learn anything if you're not working through any problems on your own.
Just as an add-on, Stewart's is definitely the best way to go for learning applied calculus as a beginner. It's EXHAUSTIVE, though I'd actually recommend the full-on "Calculus" textbook instead of "Early Transcendentals" or "Single (Multi) Variable" texts for this reason:
At the end of every chapter, there are "problems plus" that will really challenge the way you think about what you've just learned. You don't get these in the other books. They'll make you think like a mathematician or a scientist instead of a "plug-and-chugger."
And once again, I'm gonna plug Smith's "Transition to Advanced Mathematics" for an introduction to proof-writing and set theory and the most basic of analysis. http://www.amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/0495562025/ref=sr_1_1?ie=UTF8&qid=1371247275&sr=8-1&keywords=douglas+smith+transition
Though definitely get an older edition to save more money. And I realize you can't get books delivered--you can find pdf versions of older editions.......
As for the lower, pre-calculus stuff, just look to the right on this reddit for Khan Academy and just browse through the topics there. If you're as good a student as you say you are, you just need the few holes filled in and a quick refresher, and Khan is perfect for it.
Yes!
If you don't know any calculus Stewart Calculus is the typical primer in colleges. Combine this with Khan Academy for easy mode cruise control.
After that, you want to look at The Big Orange Book, which is essentially the bible for undergrad astrophysics and 100% useful beyond that. This book could, alone, tell you everything you need to know.
As for other topics like differential equations and linear algebra you can shop around. I liked Linear Algebra Done Right for linear personally. No recommendations from me on differential equations though, never found a book that I loved.
Two things:
http://www.youtube.com/user/khanacademy#p/c/19E79A0638C8D449
(I dunno why more people here don't seem to know about it).
Personally I'd recommend these two:
-http://www.amazon.com/gp/product/0470073330/ref=pd_lpo_k2_dp_sr_2?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0471316598&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=1S7Z2QKSMQM70SWRZQFT
-http://www.amazon.com/Calculus-Stewarts-James-Stewart/dp/0495011606/ref=sr_1_1?ie=UTF8&s=books&qid=1279124596&sr=1-1
You're probably gonna wanna go with earlier editions cuz they're way cheaper and say the same thing.
>It gives me that mental stimulation I desire and that I feel I am genuinely am good at and don't need to have talent for because no matter what, so long as I put in the effort, then I got it down.
That's exactly the right attitude to have. :)
If I can make a recommendation, pick yourself up a copy of "A Transition to Abstract Mathematics" or a similar text and start working your way through it. You start with logic tables and learn about set theory. You'll enjoy it if you are interested in the "whys" of math, and if you end up picking math as a major, it will be helpful stuff to review ahead of time.
People will give me flack for this but I think Stewart is a great text for an intro to calc, and moreover, one that a person with little math experience can feasibly use for self study. Obviously buying it new is expensive but I've heard rumors of PDF's flying around on torrent sites and stuff, and there's always a few used copies of it in like a 1 mile radius of wherever you are. Working through the first 8 chapters and maybe chapter 11 (infinite sequences and series) will give you a pretty thorough understanding of all of a first year calculus course, and the sections on multivariable calculus aren't bad either. Once you actually know some basics you'll want to find a more advanced text, but I find myself turning back to this text constantly when I need to remember how to do something basic that I've forgotten from first year.
Do the problems. You'll get stuck on lots of them. /r/learnmath is great for that—if you post a problem from this book up there you'll have a detailed answer in about 45 seconds. http://math.stackexchange.com is also great for that.
As for statistics, there's only so far you can go in traditional statistics without knowing any calculus. You can learn the extreme basics like descriptive statistics and basic probability, but at some point, probability theory requires that you know how to take a derivative or an integral, so you'll need to have those skills under your belt. So I'd start on Stewart's book and just try to work through it.
Here's mine
To understand life, I'd highly recommend this textbook that we used at university http://www.amazon.com/Campbell-Biology-Edition-Jane-Reece/dp/0321558235/ That covers cell biology and basic biology, you'll understand how the cells in your body work, how nutrition works, how medicine works, how viruses work, where biotech is today, and every page will confront you with what we "don't yet" understand too with neat little excerpts of current science every chapter. It'll give you the foundation to start seeing how life is nothing special and just machinery (maybe you should do some basic chemistry/biology stuff on KhanAcademy first though to fully appreciate what you'll read).
For math I'd recommend doing KhanAcademy aswell https://www.khanacademy.org/ and maybe a good Algebra workbook like http://www.amazon.com/The-Humongous-Book-Algebra-Problems/dp/1592577229/ and after you're comfortable with Algebra/Trig then go for calc, I like this book http://www.amazon.com/Calculus-Ron-Larson/dp/0547167024/ Don't forget the 2 workbooks so you can dig yourself out when you get stuck http://www.amazon.com/Student-Solutions-Chapters-Edwards-Calculus/dp/0547213093/ http://www.amazon.com/Student-Solutions-Chapters-Edwards-Calculus/dp/0547213107/ That covers calc1 calc2 and calc3.
Once you're getting into calc Physics is a must of course, Math can describe an infinite amount of universes but when you use it to describe our universe now you have Physics, http://www.amazon.com/University-Physics-Modern-12th/dp/0321501217/ has workbooks too that you'll definitely need since you're learning on your own.
At this point you'll have your answers and a foundation to go into advanced topics in all technical fields, this is why every university student who does a technical degree must take courses in all those 3 disciplines.
If anything at least read that biology textbook, you really won't ever have a true appreciation for the living world and you can't believe how often you'll start noticing people around you spouting terrible science. If you could actually get through all the work I mentioned above, college would be a breeze for you.
I'm a student (Junior ME) so my recommendation would be better suited over at /r/engineeringstudents but if you wanted to get started on the entry level coursework. Here's where you can start.
Calculus
http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts-Series/dp/0495011665/ref=sr_1_2?ie=UTF8&qid=1371011569&sr=8-2&keywords=stewart+calculus+6th+edition
Physics
http://www.amazon.com/Physics-Scientists-Engineers-Strategic-Approach/dp/0321516591/ref=sr_1_2?s=books&ie=UTF8&qid=1371011593&sr=1-2&keywords=knight+physics+for+scientists+and+engineers+2nd+edition
Engineering Statics / Dynamics
http://www.amazon.com/Engineering-Mechanics-Combined-Statics-Dynamics/dp/0138149291/ref=sr_1_9?s=books&ie=UTF8&qid=1371011626&sr=1-9&keywords=hibbler+statics+dynamics
Engineering Mechanics of Materials
http://www.amazon.com/Mechanics-Materials-8th-Russell-Hibbeler/dp/0136022308/ref=sr_1_1?s=books&ie=UTF8&qid=1371011680&sr=1-1&keywords=hibbler+mechanics+of+materials
It should be this one
ISBN-13: 978-1-133-11228-0
The math dept uses a custom version with black cover (but I think the content is the same). 150A covers chapters 1-6.
The name is Essential Calculus: Early Transcendentals, Custom Edition 2E, Stewart
Also, your professor probably will use Webassign.
> Is there any good book with problems/examples that I could work through in order to thoroughly prepare myself to be able to write proofs for a Real Analysis I course?
Besides Velleman's "How to Prove it," try Mathematical Proofs: A Transition to Advanced Mathematics or maybe How to Read and Do Proofs: An Introduction to Mathematical Thought Processes.
The book I used in my "Intro to Proofs" course was A Transition to Advanced Mathematics. It was pretty good, but the edition that I used had several mistakes in it. Also, it's waaaay too expensive.
Now for the unpleasantries —
Suggestions aside, the main problem here is your "thoroughly prepare myself to be able to write proofs for Real Analysis" goal. Working through a proofs book on your own will be seriously challenging, but the thought of taking Real Analysis without at least two other proofs courses under your belt is terrifying to me. I had to take "An intro to mathematical proofs" followed almost immediately by a proof-based Linear Algebra course before I was even allowed to contemplate a Real Analysis course.
Come to think of it, how in the hell are you even allowed to do this if you haven't taken a proofs course before? Are you sure this is even possible? Are prerequisites not enforced at your school? No one, and I mean no one was permitted to take Abstract Algebra or Real Analysis without the required prerequisites at my university. The only way you could get around it was by being the next Andrew Wiles.
Just to drive all this home, I was a straight-A Physics/Math major with the exception of two courses: Thermodynamics and my first proofs course. I've never worked so damn hard for a B in my life. Come to think of it, I actually recall quantum mechanics being easier than my proofs course.
I'm being sincere when I ask you to reconsider this plan. You are asking for a world of pain followed by the very real possibility of failure if you do this.
TL;DR: Unless you are remarkably sharp and have loads of time on your hands, this is probably a mistake. You should take a more elementary proofs course before tackling Real Analysis. Good luck, whatever you choose to do.
I posted this in another comment but I'm guessing this bastard?
https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552/
Just wait until you get on campus and go to your first class to purchase any books for that class. Then you will know for sure whether or not you really need the textbook instead of spending a lot of money now on a textbook you won't use at all. You won't be at a disadvantage either since you will probably not use the book at all for the first few weeks anyways, giving you a lot of time to get the right book if you really need it.
If you MUST get a book now, the textbook that most algebra and calculus classes use is Essential Calculus: Early Transcendentals (Amazon here). The demand is very high for this book so if you buy it now and find out you don't need it you could sell it to some other freshman very easily.
Easiest case is just to wait until you really know what book your class uses and if you really need it or not.
The most popular calculus book for college classes in the United States is Stewart, Calculus: Early Transcendentals. A typical Calculus II course starts somewhere in chapter 5 or 6 (picking up wherever Calculus I left off) and ends with chapter 11.
This book has answers to all of the odd-numbered exercises in the back, so it works reasonably well to read the book and then try the exercises. Typically the first 3/4 of the exercises in each section are straightforward, and the remaining 1/4 are more difficult and would only be assigned in an honors class.
The Feynman Lectures will do the job, can be pretty expensive but you can just look at the online version here.
One book that deals with classical through modern physics is Physics for Scientists and Engineers with Modern Physics by Serway & Jewett. To (re)learn intro physics, really any similar book will do, and you can always get help from online resources, of which there are many.
A good text for Modern Physics on its own is Kenneth Krane's Modern Physics. It has a lot of problems (few physics textbooks don't, and you won't learn physics easily without them) but it has none of the other superfluous things you mention.
As far as math goes, maybe try using Khan Academy or a similar resource up through precalculus. As far as calculus is concerned, I can recommend Stewart's Essential Calculus as a pretty comprehensive textbook which covers a pretty wide area. I can also highly recommend Paul's Online Math Notes to help you learn algebra through calculus and differential equations.
Holy crap OP, where do you go to school? All the topics you mentioned are (in my experience) usually split up into two separate courses (Calc II and III), and part of a third as well (the diff eq. stuff). As far as textbooks go I can only recommend what I used:
http://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/0538497904/ref=sr_1_1?ie=UTF8&qid=1418617662&sr=8-1&keywords=calculus+early+transcendentals+7th+edition
http://www.amazon.com/Calculus-Early-Transcendentals-Howard-Anton/dp/0470647698/ref=sr_1_2?ie=UTF8&qid=1418617682&sr=8-2&keywords=anton+calculus
You should spend some lovely evenings with my friend, Stewart. If you find my friend Stewart too hard on you, take some exercises from my little friend Thomas! And if you want even more fun, my friend Piskunov has some lovely exercises for you!
And ask your questions here :-)
Fundamentals of Heat and Mass Transfer by Incropera is pretty much the standard text on the subject by my understanding.
I used Hibbeler for Mechanics of Materials, but Beer is also a popular choice.
Hibbeler for dynamics as well.
Larson has a pretty good calculus book, will take you from derivatives up through multivariable.
A good resource if you feel like digging deeper is the physics forums - science and math textbook forum.
If you are asking for classics, in Algebra, for example, there are(different levels of difficulty):
Basic Algebra by Jacobson
Algebra by Lang
Algebra by MacLane/Birkhoff
Algebra by Herstein
Algebra by Artin
etc
But there are other books that are "essential" to modern readers:
Chapter 0 by Aluffi
Basic Algebra by Knapp
Algebra by Dummit/Foot
I've been kinda sorta watching it but I think he was holding up Artin's book.. not sure..
edit: Okay, the beginning of the second video confirms my guess..
From my experience, Calculus in America is taught in 2 different ways: rigorous/mathematical in nature like Calculus by Spivak and applied/simplified like the one by Larson.
Looking at the link, I dont think you need to know sets and math induction unless you are about to start learning Rigorous Calculus or Real Analysis. Also, real numbers are usually introduced in Real Analysis that comes after one's exposure to Applied/Non-Rigorous Calculus. Complex numbers are, I assume, needed in Complex Analysis that follows Real Analysis, so I wouldn't worry about sets, real/complex numbers beyond the very basics. Math induction is not needed in non-proof based/regular/non-rigorous Calculus.
From the link:
For Calc 1(applied)- again, in my experience, this is the bulk of what's usually tested in Calculus placement exams:
Solving inequalities and equations
Properties of functions
Composite functions
Polynomial functions
Rational functions
Trigonometry
Trigonometric functions and their inverses
Trigonometric identities
Conic sections
Exponential functions
Logarithmic functions
For Calc 2(applied) - I think some Calc placement exams dont even contain problems related to the concepts below, but to be sure, you, probably, should know something about them:
Sequences and series
Binomial theorem
In Calc 2(leading up to multivariate Calculus (Calc 3)). You can pick these topics up while studying pre-calc, but they are typically re-introduced in Calc 2 again:
Vectors
Parametric equations
Polar coordinates
Matrices and determinants
As for limits, I dont think they are terribly important in pre-calc. I think, some pre-calc books include them just for good measure.
If you're trying to learn calculus on your own you're better off buying a used version of either of these books for cheap (or going to a library)
http://www.amazon.com/Thomas-Calculus-11th-George-B/dp/0321185587
or Stewart: http://www.amazon.com/Calculus-Stewarts-James-Stewart/dp/0495011606/ref=sr_1_1?ie=UTF8&s=books&qid=1268447623&sr=1-1
Schaums provides basic insight, and several practice problems. If you want to understand the theory, go for Stewart or Thomas.
Check out A Transition to Advanced Mathetmatics. I took an enjoyable course with this book before starting to get deeper into my career and it was a nice primer.
Edit: .pdf version.
I know that in the long run competition math won't be relevant to graduate school, but I don't think it would hurt to acquire a broader background.
That said, are there any particular texts you would recommend? For Algebra, I've heard that Dummit and Foote and Artin are standard texts. For analysis, I've heard that Baby Rudin and also apparently the Stein-Shakarchi Princeton Lectures in Analysis series are standard texts.
Just buy a Calculus textbook and watch all of the videos on PatrickJMT/KhanAcademy.
I took the calculus sequence at a University, but 90% of what I learned was from the book and online resources.
I learned using this book by Larson. It goes out of its way to be intelligible, and I appreciated that. It's hard to recommend things sometimes, because I think everybody has a different path to understanding these topics. A lot of the time it seems you need to just keep throwing resources at it until something sticks. Good luck.
I'm really glad that helped you out, the hardest part of the transition for most math majors is going from deductive reasoning to inductive reasoning, so essentially your Calc and Linear Algebra classes to your proof based courses/Real Analysis. At my uni this is our intro to advanced math lectures, http://math.gmu.edu/~dsingman/lectf14.html , and the lectures are based off one of the best intro to proofs books,https://www.amazon.com/gp/product/1285463269/ref=ppx_yo_dt_b_asin_title_o04_s00?ie=UTF8&psc=1. These are tools i look back onto, especially when i took real analysis and abstract algebra.
https://www.amazon.com/Calculus-James-Stewart/dp/1285740629/ref=sr_1_1?ie=UTF8&qid=1484794699&sr=8-1&keywords=calculus+8th+edition
I would say that the best way to start is to pick a single book in Calculus, such as this or this or even this, and work all the way through it.
Then it is up to you; you could go straight towards Real Analysis; I recommend starting with a book that bears Intro in the name.
Or you could pursue a more collegiate curriculum and move onto Differential Equations and Linear Algebra, then Real Analysis.
I assume you are doing this all independently, so you should look at college sequences for math majors and the likes. You can mimic those, and look for online syllabi of the courses to make sure you are covering the appropriate material. This helps because it gives a nice structure to your learning.
Whatever the case, work through a calculus book, then decide what further direction you wish to take.
Calculus or Pre-calc?
For calculus, I recommend: http://www.amazon.com/Calculus-Ron-Larson/dp/1285057090/ref=sr_1_2?s=books&ie=UTF8&qid=1398268486&sr=1-2&keywords=larson+edwards+calculus
It's written by the same guy who does the Calculus 1 and 2 lectures for The Teaching Company.
He doesn't address the problem I mentioned in my previous post, but I still think this is a much more concise book.
i can back this assessment up, as i used this text for the exact same thing. http://www.amazon.com/Calculus-Early-Transcendentals-Stewarts-Series/dp/0495011665 a broad text, well explained, with many helpful practice problems.
http://www.khanacademy.org/ is a pretty solid resource up through Linear Algebra. I'd recommend picking up a textbook in each subject so that you have a good list of examples and problems to work through to supplement Khan Academy. A used older edition of Stewart's Calculus would do good, it has everything as the newer ones and it is the standard calc textbook. Remember to keep doing problems, and don't stop, especially on the ones that are giving you the biggest headache! If you have any questions or problems ask /r/cheatatmathhomework or /r/learnmath.
Once you have an understanding of the basics, the MIT Open Courseware is a good source.
I've heard some good things about Michael Artin's book (http://www.amazon.com/Algebra-Michael-Artin/dp/0130047635).
Game Engine:
Game Engine Architecture by Jason Gregory, best you can get.
Game Coding Complete by Mike McShaffry. The book goes over the whole of making a game from start to finish, so it's a great way to learn the interaction the engine has with the gameplay code. Though, I admit I also am not a particular fan of his coding style, but have found ways around it. The boost library adds some complexity that makes the code more terse. The 4th edition made a point of not using it after many met with some difficulty with it in the 3rd edition. The book also uses DXUT to abstract the DirectX functionality necessary to render things on screen. Although that is one approach, I found that getting DXUT set up properly can be somewhat of a pain, and the abstraction hides really interesting details about the whole task of 3D rendering. You have a strong background in graphics, so you will probably be better served by more direct access to the DirectX API calls. This leads into my suggestion for Introduction to 3D Game Programming with DirectX10 (or DirectX11).
C++:
C++ Pocket Reference by Kyle Loudon
I remember reading that it takes years if not decades to become a master at C++. You have a lot of C++ experience, so you might be better served by a small reference book than a large textbook. I like having this around to reference the features that I use less often. Example:
namespace
{
//code here
}
is an unnamed namespace, which is a preferred method for declaring functions or variables with file scope. You don't see this too often in sample textbook code, but it will crop up from time to time in samples from other programmers on the web. It's $10 or so, and I find it faster and handier than standard online documentation.
Math:
You have a solid graphics background, but just in case you need good references for math:
3D Math Primer
Mathematics for 3D Game Programming
Also, really advanced lighting techniques stretch into the field of Multivariate Calculus. Calculus: Early Transcendentals Chapters >= 11 fall in that field.
Rendering:
Introduction to 3D Game Programming with DirectX10 by Frank. D. Luna.
You should probably get the DirectX11 version when it is available, not because it's newer, not because DirectX10 is obsolete (it's not yet), but because the new DirectX11 book has a chapter on animation. The directX 10 book sorely lacks it. But your solid graphics background may make this obsolete for you.
3D Game Engine Architecture (with Wild Magic) by David H. Eberly is a good book with a lot of parallels to Game Engine Architecture, but focuses much more on the 3D rendering portion of the engine, so you get a better depth of knowledge for rendering in the context of a game engine. I haven't had a chance to read much of this one, so I can't be sure of how useful it is just yet. I also haven't had the pleasure of obtaining its sister book 3D Game Engine Design.
Given your strong graphics background, you will probably want to go past the basics and get to the really nifty stuff. Real-Time Rendering, Third Edition by Tomas Akenine-Moller, Eric Haines, Naty Hoffman is a good book of the more advanced techniques, so you might look there for material to push your graphics knowledge boundaries.
Software Engineering:
I don't have a good book to suggest for this topic, so hopefully another redditor will follow up on this.
If you haven't already, be sure to read about software engineering. It teaches you how to design a process for development, the stages involved, effective methodologies for making and tracking progress, and all sorts of information on things that make programming and software development easier. Not all of it will be useful if you are a one man team, because software engineering is a discipline created around teams, but much of it still applies and will help you stay on track, know when you've been derailed, and help you make decisions that get you back on. Also, patterns. Patterns are great.
Note: I would not suggest Software Engineering for Game Developers. It's an ok book, but I've seen better, the structure doesn't seem to flow well (for me at least), and it seems to be missing some important topics, like user stories, Rational Unified Process, or Feature-Driven Development (I think Mojang does this, but I don't know for sure). Maybe those topics aren't very important for game development directly, but I've always found user stories to be useful.
Software Engineering in general will prove to be a useful field when you are developing your engine, and even more so if you have a team. Take a look at This article to get small taste of what Software Engineering is about.
Why so many books?
Game Engines are a collection of different systems and subsystems used in making games. Each system has its own background, perspective, concepts, and can be referred to from multiple angles. I like Game Engine Architecture's structure for showing an engine as a whole. Luna's DirectX10 book has a better Timer class. The DirectX book also has better explanations of the low-level rendering processes than Coding Complete or Engine Architecture. Engine Architecture and Game Coding Complete touch on Software Engineering, but not in great depth, which is important for team development. So I find that Game Coding Complete and Game Engine Architecture are your go to books, but in some cases only provide a surface layer understanding of some system, which isn't enough to implement your own engine on. The other books are listed here because I feel they provide a valuable supplement and more in depth explanations that will be useful when developing your engine.
tldr: What Valken and SpooderW said.
On the topic of XNA, anyone know a good XNA book? I have XNA Unleashed 3.0, but it's somewhat out of date to the new XNA 4.0. The best looking up-to-date one seems to be Learning XNA 4.0: Game Development for the PC, Xbox 360, and Windows Phone 7 . I have the 3.0 version of this book, and it's well done.
*****
Source: Doing an Independent Study in Game Engine Development. I asked this same question months ago, did my research, got most of the books listed here, and omitted ones that didn't have much usefulness. Thought I would share my research, hope you find it useful.
> btw ce crezi de masterul asta de la unibuc http://fmi.unibuc.ro/ro/pdf/2008/curs_master/informatica/4InteligentaArtificialaEnachescuSite.pdf , e din 2008,nu am gasit o varianta mai buna.Daca voi avea posibilitatea sa fiu acceptat l;a o facultate mai moderna care face cercetare din afara o voi face,dar mai intai trebuie sa capat o diploma din Romania).
Acum, trebuie sa intelegi ca ML si AI sunt 2 lucruri diferite. AI includes ML, si ce ai tu aici e un master general de AI. Nu pot sa iti spun cat de bun e masterul, dar vad ca faci 1 curs de ML doar in anul 2, ceea ce pentru mine ar fi un motiv sa nu il fac. Information retrieval si NLP sunt interesante, dar eu as incerca sa invat ML la nivel teoretic first, si apoi sa abordez probleme specifice domeniilor.
> Eu ma gandeam ca Unibuc e mai potrivit pt ca la Poli voi face multa electronica si programare low-level si nu cred ca le voi folosi
Ar putea fi utile daca te gandesti la un moment dat ca te intereseaza mai degraba sa fii Research engineer si sa nu lucrezi atat de mult pe teorie, cat pe implementare. Toate librariile de scientific programming sunt implementate in C/C++. Dar pe langa asta, in general programarea low-level ar fi interesant sa o inveti pentru ca te ajuta sa intelegi cum functioneaza lucrurile at a more basic level, fara x abstractii construite pentru a fi totul beginner-friendly. Daca nu vrei sa continui cu asta dupa 1-2 cursuri e ok, tot cred ca iti va folosi mai incolo. Sa inveti python si c++ in paralel e un challenge interesant :).
> Va veni vacanta de vara si voi avea mult timp liber si vreau sa ma apuc de machine learning de-acum.Ce crezi de planul asta de invatare?
Iti va lua mai mult decat 1 vara sa termini ce ai listat aici. Sfatul meu ar fi sa imbini programare aplicata cu matematica. Cursurile sunt ok, dar eu pentru matematica as incepe cu single variable calculus -> multiple variable calculus inainte de altceva (daca ai cunostintele necesare sa abordezi cursul). Uite o carte pe care ti-o recomand: https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552
Are in jur de 8 sectiuni care reprezinta pre-requisites (lucruri pe care ar trebui sa le stii inainte sa abordezi cartea), algebra, geometrie de baza, etc. Fiecare invata diferit, eu prefer cartile.
Legat de programare, incearca sa faci probleme de aici: https://projecteuler.net/, te va ajuta mai incolo :). Si daca te plictisesti incearca construiesti lucruri care ti-ar fi utile. Vei invata destule din proiecte de genul.
It is an integral of the variable x, as you point out. You can refer to, this book
I'd recommend hitting up somewhere like half-price books and grabbing a textbook for like $10-$15. I purchased this book for probably $12 when I needed to brush up. I know it's not online, but it will provide good direction, offer a solid foundation, provide sample problems to test your knowledge, and can easily be supplemented by online materials. As someone else mentioned, Khan Academy is also great, but I would highly recommend using them as a supplement, and using a book as your base.
> I can solve though but the thought why i am doing this is always alarming inside, go and ask any teacher or students as why they do these maths? They will say it's for Grades!
Eek, you have a terrible history of teachers.
>Don't know how many students give up maths just because of wrong Teacher.
For sure.
Starting with calculus/analysis, the book most undergraduate students in America start with is this one. Not every concept starts with real-life examples, but every chapter and section includes actual real-life examples.
Honestly, in order to get a feel for whether you like Math, I'd suggest taking a look at the textbook for MATH 290 (Intro to Adv. Math): A Transition to Advanced Mathematics by Smith et. al. (8th ed. on Amazon, Free 7th ed. PDF). Go through the first few chapters and prove some simple statements (similar to what you'd do in CS 330, but taught in a more sensible way).
Note: Math isn't tedious calculations, endless derivatives and logarithms and algebraic manipulation, and solving absurd word problems. Math is about making statements and developing abstract concepts, seeing the links between abstract concepts, and being able to rigorously prove these statements so that someone else can read and understand it.
Statistics is a specific field of math focused on how to collect, analyze, interpret, and present data. Statistics is used to conduct the US census, fight fraud, determine if a product or drug is actually effective, "teach" computers to recognize tumors or deadly mushrooms from benign ones, model hurricanes and predict storm surge, and all kinds of interesting stuff. You're required to take STAT 344 as part of the CS degree, and I think it actually gives you a good understanding of whether you like statistics (although the course also covers probability).
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Note that while "beginner maths"^1 are your basic geometry, trignometry, algebra, and calculus. None of these skills are required to understand that MATH 290 textbook. We have calculators for that.
Math is shared language for precisely describing the world. You observe something^2, come up with a general way to describe it, and then you can study it or link it to other concepts. Math is exciting because it helps you discover hidden meaning in what is around you.
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^1 In fact, prior to taking MATH 290 (Intro to Adv. Math), math students have already taken MATH 113 (Calculus I) and II and MATH 125 (Discrete Math). Many have also taken MATH 203 (Linear Algebra) and MATH 214 (Differential Equations).
^2 If you've ever asked yourself a question like
then you're closer to what math actually is.
What text are you using?
Edit: Most calc II or multivariable textbooks that I've encountered (e.g.: this one, this one, this one, or this one) are full of examples, problems, and sections dealing with physical applications, if that's what you mean by outside the classroom.
From what I recollect, Calc II was mostly about developing facility with integration techniques, with some extensions of the concept of integration to boot. Although some of the material may seem to be of little relevance, think of it as an important stepping stone. It is preparing you for some super interesting subjects (like line integrals on vector fields!) that are used to model physical systems.
Yes, I do! I would highly suggest using Paul's Online Math Notes. I've never used it to specifically try to teach myself an entire course but he's always been an excellent source for when I was ever stuck. Also be warned: Paul assumes you remember some bits of calculus 2!
That being said: download/buy/rent/whatever yourself a textbook! I used this textbook when I took the course. Its expensive because it has calculus 1, 2, and 3 in one giant book (so it would be good for reviewing calculus 2 if you'd like). It's a good textbook (not amazing though) with a nice variety of problems.
I've taught myself a number of courses but calculus was not any of them. I don't have any specific advice for you other than stressing that you should always apply what you learn - don't settle for "oh, I understand this section. I'll just move on to the next section!" w/o first solving at least a dozen or so problems.
Good luck!
There's no single book that's right for everyone: a suitable book will depend upon (1) your current background, (2) the material you want to study, (3) the level at which you want to study it (e.g., undergraduate- versus graduate-level), and (4) the "flavor" of book you prefer, so to speak. (E.g., do you want lots of worked-out examples? Plenty of exercises? Something which will be useful as a reference book later on?)
That said, here's a preliminary list of titles, many of which inevitably get recommended for requests like yours:
Good luck finding something useful!
I took Calc I & II last semesters and we used [this textbook] (https://www.amazon.com/Calculus-Ron-Larson/dp/1285057090). Check again in a month on coursebook, but you'll most likely use the same book.
Math texts are among the most egregious examples of unnecessarily updated texts. Almost none of the math you'll learn as an undergrad has changed in my lifetime, but students have to buy the newest version just so they can have the right homework problems. Stewart's text is at version 8, and you can [buy it on Amazon for $183] (https://www.amazon.com/Calculus-James-Stewart/dp/1285740629/ref=pd_sbs_14_1?_encoding=UTF8&pd_rd_i=1285740629&pd_rd_r=JVSPPXJ3JZSTMBTMY7ZA&pd_rd_w=y7iOT&pd_rd_wg=2XT4J&psc=1&refRID=JVSPPXJ3JZSTMBTMY7ZA). I just looked and found a used copy of the 7th edition for $12. It's so cheap because student's cant use the damned thing. I used Thomas and Finney's book thirty years ago, and there haven't been any developments in Calculus since then that are relevant to a Freshman Engineering Major. The teacher of my Functional Analysis class in grad school was fed up with this, so we used Riesz and Sz.-Nagy's Dover Edition. This was a graduate-level math class, and we were able to use a text that was decades old.
Michael Artin's Algebra's first few chapters is probably one of the best explanations of linear algebra that you'll get.
http://www.amazon.com/Algebra-Michael-Artin/dp/0130047635
Honestly, Calculus by Ron Larson. You can get a previous edition(I used the 9th when I was learning) for cheaper. This is the clearest Calculus book I have ever read at Stewart's level (I textbook I detest btw). Larson also has a website http://www.calcchat.com/ where he has step by step solutions to all odd problems, so very very good for self learning.
Here is an actual blog post that conveys the width of the text box better. Here is a Tufte-inspired LaTeX package that is nice for writing papers and displaying side-notes; it is not necessary for now but will be useful later on. To use it, create a tex file and type the following:
\documentclass{article}
\usepackage{tufte-latex}
\begin{document}
blah blah blah
\end{document}
But don't worry about it too much; for now, just look at the Sample handout to get a sense for what good design looks like.
I mention AoPS because they have good problem-solving books and will deepen your understanding of the material, plus there is an emphasis on proof-writing when solving USA(J)MO and harder problems. Their community and resources tabs have many useful things, including a LaTeX tutorial.
Free intro to proofs books/course notes are a google search away and videos on youtube/etc too. You can also get a free library membership as a community member at a nearby university to check out books. Consider Aluffi's notes, Chartrand, Smith et al, etc.
You can also look into Analysis with intro to proof, a student-friendly approach to abstract algebra, an illustrated theory of numbers, visual group theory, and visual complex analysis to get some motivation. It is difficult to learn math on your own, but it is fulfilling once you get it. Read a proof, try to break it down into your own words, then connect it with what you already know.
Feel free to PM me v2 of your proof :)
Start here.
Then get through the first half of this. That will give you the knowledge you need to work through this book. Then you can go back to the second book and finish it which will give you the background you need to work through this book.
​
But you won't. You'd rather believe some idiot on youtube than put in the effort to learn the beautifully elegant way the world actually works.
> The 14th is brand new this year, so I'd take that single one-star review with a huge grain of salt.
Yes you raise a good point. One review is usually not a good metric.
>So it's possible that they botched it up pretty badly and Thomas is rolling in his grave.
Looks like this edition was released in January. I guess we will find out at the end of this semester as more reviews start to roll in.
I was always a fan of the Stewart book to be honest. It was lovely to go through.
A lesser known book Calculus by Larson and Edwards is also a personal favorite. Have you used the Stewart or Larson books?
>I recommend a riot, burning the Pearson HQ to the ground
That is just yet another reason. There are already many reasons to riot Pearson already. :)
A Transition to Advanced Mathematics, I think
For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.
For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.
While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.
So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.
Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.
A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.
These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.
Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.
Good luck on your journey!
Hi there,
It'd be a good idea to know what your level of mathematics is like. I assume you know basic set theory? (I assume this is needed to analyze music from the second viennese school - but how detailed is the set theory you learn? Are there proofs?). What other maths do you have knowledge of? I believe the standard algebra book is Artin's but this may be too hard/dense for you. I can think of some easier books off the top of my head, but they start off with ring/fields instead of groups (such as the Hungerford)...
Just curious, do you have any suggestions on what a random person can read to learn about transformational theory on the net besides wikipedia?
Edit: Random googling found this. Seems like a good start for both mathematicians to learn about 20th century music theory and musicians to learn about set theory/algebra.
My school used this for the first two years of calculus.
Well, here are links:
​
https://www.khanacademy.org/math/multivariable-calculus
https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/
https://www.amazon.com/Multivariable-Calculus-James-Stewart/dp/1305266641/ref=sr_1_7?keywords=stewart+calculus&qid=1556212324&s=gateway&sr=8-7
If you stopped with calc I, you may not have really finished single variable. You should be able to find the single variable resources by poking around at the same three sites.
(Also, look for an older, cheaper edition of Stewart)
One thing I found useful for doing this is Stewart's Calculus (many people will disagree with me here, but it was my old Calc book, so I didn't have to buy a new one, and I thought it was pretty decent). Don't worry about buying the latest version. you can probably find an old one in a used book store, or ebay or something, which will save you some bucks. The thing that kills Calc students is their poor algebra, so make sure you are rock-solid on that. You should be able to solve linear equations, quadratic equations, rational equations, and equations involving square-roots without a problem. You should also be able to graph all of these, and you should have a good understanding of exponents and logs. Don't spend much time reading the book, spend your time practicing, doing problem after problem until you really nail each one. If you can find a study-buddy, this will help a lot, as they will be able to point out where you are going wrong, and you will be able to teach them things (which is one of the best ways to learn).
Anyway, that's just some random advice, but I hope it helps. Good luck!
Calculus by James Stewart.
http://www.amazon.com/Calculus-James-Stewart/dp/0538497815
I'm about 90% sure that your calculus course will use this book.
I would go back and refresh yourself on your college algebra and trigonometry. Knowing things like your identities and how to move things around/re-write a term algebraically is about 50% of mastering the classes. In some of the more complex differentiation and integrals later on, simplifying the equation you start with helps immensely.
I recommend purchasing yourself a copy of this book: https://www.amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/0495562025
Chapter 0 is especially great, as it guides you through some of the basic grammar of mathematics. Most of the material is seen in some form or another in 115A(H), but I personally found this book to be a much better introduction to the upper division courses.
Depends on the market depths, for a lot of books, there may be a couple low priced books where a few purchases will raise the price pretty significantly. I think a lot of booksellers have repricers that don't work very effectively where they'lll lower the price over time until it sells, and there really isnt a market for text books except for at the beginning of semesters.
http://www.amazon.com/gp/offer-listing/1285741552/ref=olp_f_primeEligible?ie=UTF8&f_primeEligible=true
On that book, which is a pretty widely used text, If they sell about 5 books, the price rises almost $70.
For a very good textbook, I would recommend Calculus Early transcendentals by Stewart. He goes through every concept in single variable calculus (there's also a version with multi variable calculus) and proves almost every concept he teaches. Its one of my favorite textbooks in general.
Hello! I'm interested in trying to cultivate a better understanding/interest/mastery of mathematics for myself. For some context:
 
To be frank, Math has always been my least favorite subject. I do love learning, and my primary interests are Animation, Literature, History, Philosophy, Politics, Ecology & Biology. (I'm a Digital Media Major with an Evolutionary Biology minor) Throughout highschool I started off in the "honors" section with Algebra I, Geometry, and Algebra II. (Although, it was a small school, most of the really "excelling" students either doubled up with Geometry early on or qualified to skip Algebra I, meaning that most of the students I was around - as per Honors English, Bio, etc - were taking Math courses a grade ahead of me, taking Algebra II while I took Geometry, Pre-Calc while I took Algebra II, and AP/BC Calc/Calc I while I took Pre-Calc)
By my senior year though, I took a level down, and took Pre-Calculus in the "advanced" level. Not the lowest, that would be "College Prep," (man, Honors, Advanced, and College Prep - those are some really condescending names lol - of course in Junior & Senior year the APs open up, so all the kids who were in Honors went on to APs, and Honors became a bit lower in standard from that point on) but since I had never been doing great in Math I decided to take it a bit easier as I focused on other things.
So my point is, throughout High School I never really grappled with Math outside of necessity for completing courses, I never did all that well (I mean, grade-wise I was fine, Cs, Bs and occasional As) and pretty much forgot much of it after I needed to.
Currently I'm a sophmore in University. For my first year I kinda skirted around taking Math, since I had never done that well & hadn't enjoyed it much, so I wound up taking Statistics second semester of freshman year. I did okay, I got a C+ which is one of my worse grades, but considering my skills in the subject was acceptable. My professor was well-meaning and helpful outside of classes, but she had a very thick accent & I was very distracted for much of that semester.
Now this semester I'm taking Applied Finite Mathematics, and am doing alright. Much of the content so far has been a retread, but that's fine for me since I forgot most of the stuff & the presentation is far better this time, it's sinking in quite a bit easier. So far we've been going over the basics of Set Theory, Probability, Permutations, and some other stuff - kinda slowly tbh.
 
Well that was quite a bit of a preamble, tl;dr I was never all that good at or interested in math. However, I want to foster a healthier engagement with mathematics and so far have found entrance points of interest in discussions on the history and philosophy of mathematics. I think I could come to a better understanding and maybe even appreciation for math if I studied it on my own in some fashion.
So I've been looking into it, and I see that Dover publishes quite a range of affordable, slightly old math textbooks. Now, considering my background, (I am probably quite rusty but somewhat secure in Elementary Algebra, and to be honest I would not trust anything I could vaguely remember from 2 years ago in "Advanced" Pre-Calculus) what would be a good book to try and read/practice with/work through to make math 1) more approachable to me, 2) get a better and more rewarding understanding by attacking the stuff on my own, and/or 3) broaden my knowledge and ability in various math subjects?
Here are some interesting ones I've found via cursory search, I've so far just been looking at Dover's selections but feel free to recommend other stuff, just keep in mind I'd have to keep a rather small budget, especially since this is really on the side (considering my course of study, I really won't have to take any more math courses):
Prelude to Mathematics
A Book of Set Theory - More relevant to my current course & have heard good things about it
Linear Algebra
Number Theory
A Book of Abstract Algebra
Basic Algebra I
Calculus: An Intuitive and Physical Approach
Probability Theory: A Concise Course
A Course on Group Theory
Elementary Functional Analysis
pre-cal: http://www.amazon.com/Precalculus-5th-Edition-Robert-Blitzer/dp/0321837347
calculus: http://www.amazon.com/Calculus-Ron-Larson/dp/1285057090
Most schools just use 1 textbook for calc 1-3 : http://www.amazon.com/Calculus-James-Stewart/dp/0538497815
Doesn't really matter which edition you get, you're still going to suffer through it.
A popular other book recommended by math majors/professors is
http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918
You can get the pdf on "certain websites."
Videos will make you lazy and you will likely lose focus and turn to reddit or games or whatever because the professors can be really boring. Just stay focused on the text.
"Just do it."
https://www.amazon.com/Calculus-James-Stewart/dp/1285740629/ref=sr_1_2?ie=UTF8&qid=1466199140&sr=8-2&keywords=james+stewart+calculus+8th+edition
It covers Calculus 1-3. I have a downloaded version from a friend of the whole book.
All I know is that they're no longer doing Fitzpatrick or Chartrand (according to what a professor told me). Here's the new book. I think it's possible the course will be less analysis-focused. I think they should incorporate some abstract algebra into it. This goes into effect next semester by the way.
We did the same. http://www.amazon.com/Calculus-Concepts-Contexts-Stewarts/dp/0495557420
nice, we're using a book by the same guy.
I'm currently working through Munkres' book on Topology, and I am using the video lectures found here. I know these are in an annoying form factor, but, trust me, these are the only videos that go into any depth you will find on the internet. They use Munkres, too, which is a plus.
On the same site are video lectures for Algebraic Topology. For this, I definitely recommend buying Artin's "Algebra" (1st edition can be found cheaply, and I don't think there's really any significant difference from 2nd), and watch these video lectures by Harvard. Then, you can finally move on to the Algebraic Topology video lectures which uses the free textbook "Algebraic Topology" by Allen Hatcher.
Hope this helps.
College books are also much more expensive in the USA than in Europe.
For example:
$152.71
VS
£43.62($68.03)
$146.26 VS
£44.34($69.16)
Awesome, I will take a look at that. Here is the book I have to teach myself with (used it for Calculus 2 a year ago). It seems like a solid book.
Does your Calc II text book not cover Calc III material as well? Most books tend to be about 800-900 pages and cover the entire calculus curriculum.
I don't have any good recommendations because they're all pretty much the same to me (with only minor idiosyncrasies). The book that the schools use is largely based on the contract they have with various publishers, and not because it is demonstrably better in any qualitative way.
This was the book I used (well, I used the fourth edition), and older editions are super cheap if you look around for them. I like(d) it just fine, and I still pull examples from it for my students because it isn't the book that they use.
I found Calculus from Larson and Edwards pretty good.
That doesn't really convey the fact that this is actually Prerequisite Algebra. This is math that you should know before entering college. Just saying "basic algebra" gives the impression that this is the first level.
On the other hand, Basic Algebra can mean "set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra." Context is everything, I suppose.
Stewart, Larson, Rogawski
For calc MATH 1300/1014 and 1310/1014 you need , buy it new from the bookstore cause you will need the online code for assignments also it’s useful for calc 3 if you wanna take that. Man Wong is a good prof I had him for both 1300 and 13010
For EECS 1019 you need it’s not that useful and PDF can be found online for free and no online assignments so no need to buy it new. I had Zhihua Chang he’s a new prof but really nice but his lectures are boring. Trev tutor on YouTube is really helping with the course.
For Math 1025/1021 you need I found the book helpful but unlike calc some profs tend not to use this book so I’d hold out of buying it but most profs use lyryz which is an online assignment program so you will need to buy that. I had Paul Skoufranis, amazing prof but had tests. The book is also useful for linear 2 but again depend if the prof uses it
For EECS 1022 you need
It’s a good book and the guy you wrote it teaches the class.
PM if you have any other questions
I would suggest combining the linear algebra and abstract algebra text into Artin's text. I have found it to be a very good text on algebra with a heavy emphasis on the theory of linear algebra. I glanced through Hungerford's text and didn't take to it. Too verbose with too many examples.
I second the Rudin and Munkres. I found that reading through Hocking and Young's text helped me get the intuition i needed to plow through Munkres.
I like this calculus book: https://www.amazon.com/Calculus-7th-James-Stewart/dp/0538497815
And this is Halliday and Resnick https://www.amazon.com/Fundamentals-Physics-David-Halliday/dp/111823071X/ref=sr_1_3?crid=9SK20IQF11Z5&keywords=halliday+and+resnick+fundamentals+of+physics&qid=1567697861&s=books&sprefix=hallida%2Cstripbooks%2C124&sr=1-3
I went ahead and grabbed a copy of this.
If you want a gentler introduction to calculus, with many examples, lots of intuition, diagrams, and nicer explanations, take any edition of James Stewart's Calculus - Early Transcendentals.
If you feel up to a serious challenge and want to study it as a mathematician would, get Michael Spivak's Calculus.
Isn't that true of any subject one likes?
Regardless, besides the Linear Algebra textbook, here are some books you should look at as well. These should give you a taste of what your introductory classes might be:
http://www.amazon.in/Transition-Advanced-Mathematics-Survey-Course/dp/0195310764
http://www.amazon.in/Transition-Advanced-Mathematics-Douglas-Smith/dp/0495562025
PM me if you want pdfs.
Hey, sorry, just saw this. Yeah that's exactly what it is.
My professor uses a different one of Stewart's books instead of Early Transcendentals like UT Calc. I only co-enrolled because I knew I don't wanna do anything Calc heavy as my major, but I've tried some of my roommate's problems and been able to do them (with a bit more effort). If I were to change my major and take Calc 3 at UT I'd probably refresh my Pre-Cal with a CE credit over the summer before
Basic Algebra? I hope he uses Jacobson's textbook :D
Textbooks in the US are priced for what students will pay, not for their actual cost, because the textbook market isn't a free market for students. You either buy the course's reccomended textbook, or find some other way to access the material. You can't shop between different publishers of the same book, unless you start looking at international editions.
>Paying for content btw
I also have this one (10th ed) but its not the one you want :/ https://www.amazon.com/Calculus-Ron-Larson/dp/1285057090
Barron's for gov and Calc ab. I would say James Stewart for calculus. Amazon should have his Calc book for cheap price https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/0495011665/ just read the chapters and do the problems. Khan academy is useful.
Looking at some books on amazon.ca, and the paperback and loose leaf versions are more expensive by a considerable amount.
you do know that a digital copy of the text book isn't free. And no you can't use the price for a digital copy that you can buy for personal use. There would be a rental charge. The calc book I used for 3 semester of calculus in College is $32/semester to rent. so that means schools are probably paying round $50/year for each digital copy of a text book.
So if you think a school book costs $250 it becomes cheaper than rental after the 5th year (not even including the increased cost of the chromebook and "insurance" required by the student.
Rental
https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart-ebook/dp/B00T9X7THG/ref=sr_1_6?s=digital-text&ie=UTF8&qid=1536864274&sr=1-6
physical copy
https://www.amazon.com/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552/ref=mt_hardcover?_encoding=UTF8&me=&qid=1536864274
http://www.amazon.com/Calculus-7th-Edition-James-Stewart/dp/0538497815
King of the formulaic problems.
I had a stellar professor and a great book. I thought it was a breeze. I used this book in undergrad: http://www.amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/0618783768/ref=sr_1_25?ie=UTF8&qid=1421682001&sr=8-25&keywords=linear+algebra
As far as notation: it will change from book to book. Learn as you go. I certainly didn't have a class or a book dedicated to the notation of mathematics. Generally the author will briefly explain their notation as they introduce the topic.
https://www.amazon.ca/Calculus-Early-Transcendentals-James-Stewart/dp/1285741552
Pretty sure it's this one. You should be able to find a pdf online.
I used a book by Larson and Falvo called Elementary Linear Algebra. So far the book was really good at explaining every topic.
My recommendation, get a Calculus book like this: Calculus by Larson. It explains everything from the beginning (analytical geometry) and with your algebra background you should understand it. Study section by section.
In one year you should have covered to Integral Calculus single variable. If you get stuck with some topic, post your question here!
Good luck!
I strongly suggest you take your time learning calculus, because anything you don't grasp completely will come back to haunt you.
But the good news is that there are lots of great resources you can use. MIT OCW has a full course with lectures, notes, and exams. Here are three free online books. If you're looking to buy a textbook, some good choices are Thomas, Stewart, and Spivak. (You can find dirt-cheap copies of older editions at abebooks.com.)
If you want more guidance, another great place to find it is at /r/learnmath.
Apart from the other good advice in this thread, if you're able to invest some money, I've heard wonderful things about this book.
It sounds like you had a really shitty teacher. Bad teachers can fuck with your confidence. But then, you already know that. I know it's easy for me to say, but: don't let that get in the way of learning math. There's nothing wrong with you. I promise you're capable of learning algebra.
There's also a /r/learnmath subreddit where you can ask questions about particular math problems.
Finally, I'm curious: does a problem like "Solve for x: 5 + x = 17" make sense to you (and would you be able to answer it)? If not, I'd be happy to write a few paragraphs about that. Maybe that's what you need to get started.
Cool.
Linear Algebra Don't waste your time with anything other than Lay, pretty much. Sounds like you're 100% new to LinAlg (it's not about polynomial equations) so it may be a bit tough to get off the ground working by yourself, but not impossible. It'd be worth finding a MOOC on the subject, there should be plenty. Otherwise, it's a pretty standard freshman maths course and a lot of people struggle with it (not because it's hard, just because it's different to HS maths), so there's a ton of resources on the internet.
Calculus Kinda just gotta slog away with where you're at tbh. I had Stewart as a freshman, didn't think it was overly great though. Still, that's the kind of level you need, so search for "alternatives to Stewart calculus" and anything that comes up should be appropriate. I wouldn't be able to tell you which to pick though.
Stats Basically, completing both of the above is pretty much a prerequisite for being able to understand linear regression properly, so don't expect to gain much by diving straight into stats. You could probably find a "business analytics" style textbook that would let you do more stats without understanding what's really going on under the hood, but if you want to stick with it in the long term you'll benefit more from getting stuff right at the beginning.
If the "Early Transcendentals" book does not have "Single-Variable" or "Multi-Variable" in its name, then it has all of the content of both books; if it does have "Single-Variable" in its name, then it might share a chapter with "Multi-Variable" but that's it.
The response by /u/jimmy_rigger was made as if you were asking about a textbook explicitly labeled as "Single-Variable", and my reply pointed out that you weren't.
---
You can look inside the books to see for yourself:
I even noticed almost the same sequence of chapters in a competing textbook (Thomas), except that it puts infinite series before polar/parametric (chapters 10 and 11).
The E101 "handbook" is made by NC State, so yeah, that's only going to be on the bookstore. That thing was useless though, and I'm pretty sure I just threw it away.
For EC 201, you might have been told to buy a custom book. I did and my friends who took it also did. When the teacher makes a "custom" book, you have to buy it through the bookstore. You also can just buy the standard version, but the organization of chapters may be different (and often, some chapters are taken out of from the standard version). But then again, since the professor usually removes stuff, it may actually end up cheaper to buy the custom one.
As for your Calc 3 book, is this the one who were told to buy: http://www.amazon.com/Calculus-Concepts-Contexts-Stewarts-Series/dp/0495557420/ref=sr_1_1?ie=UTF8&qid=1376233469&sr=8-1&keywords=stewart+calculus+concepts+and+contexts. That's the one I used last year. Not sure why you couldn't find that.
But for future reference, don't buy your books before classes. I did freshmen year and it was a mistake. If you are reasonably smart, you will never open your EC 201 textbook. I only used my Calc 3 book a couple of times as well. I did great in both classes and could have done so without the books easily.
That depends on your own level, your goals and your ambition. For example, OP wants to learn machine learning. Assuming OP's highschool math is solid, it might be possible for OP to simply download pytorch and immediately start programming neural networks without worrying too much about the hardcore math in the background.
On the other hand, if OP is more serious about improving as a mathematician, and assuming nothing but highschool math, I would start with linear algebra and differential and integral calculus. The famous professor Gil Strang has an excellent book on linear algebra, which is strangely available online. For differential and integral calculus, probably the standard reference is Stewart's book. At this point, OP would have all the basic things needed to start with machine learning. I'm not aware of the literature for machine learning so I can't recommend any specific books.
If OP wanted to get sidetracked learning more things before plunging into machine learning then the obvious choice would be Scientific Computing (my friends wrote an excellent book on the subject). Scientific Computing is the science of calculating things using computers and supercomputers. In addition, the area of Mathematical Optimization is good to know because Stochastic Gradient Descent is omnipresent in machine learning, but I don't know enough about optimization to recommend a book. There is Boyd and Vandenberghe but that is only for convex optimization. Some more areas that are related and useful are Probability and Statistics.
Sweet. I think the best curriculum to approach this with, assuming you're in this for the long haul, would be to start with building a good understanding of calculus, cover basic classical mechanics, then cover electricity and magnetism, and finally quantum mechanics. I'm going to leave math and mechanics mostly for someone else, because no textbooks come to mind at the moment. I'll leave you with three books though:
For Math, unless someone else comes up with something better, the bible is Stewart's Calculus
The other two are by the same author:
Griffith's Introduction to Electrodynamics
Griffith's Introduction to Quantum Mechanics
I think these are entirely reasonable to read cover to cover, work through problems in, and come out with somewhere near an undergraduate level understanding. Be careful not to rush things. One of the biggest barriers I've run into trying to learn physics independently is to try and approach subjects I don't have the background for yet: it can be a massive waste of time. If you really want to learn physics in its true mathematical form, read the books chapter by chapter, make sure you understand things before moving on, and do problems from the books. I'd recommend buying a copy of the solutions manuals for these books as well. It can also be helpful to look up the website for various courses from any university and reference their problem sets/solutions.
Good luck!
It's this one! http://www.amazon.com/Essential-Calculus-Transcendentals-James-Stewart/dp/1133112285
Okay.. Someone had to do it.. right?
Statistics for business and economics ~$131.15 Used and ~$188.39 New.
Principles & Practices of Physics v1 hardcover ~$51.55 Used and ~$164.02 New.
Chemistry - The Molecular Nature... ~$124.00 Used and ~$239.87 New.
Principles & Practices of Physics v2 ~$129.74 Used and ~$126.78 New.
Differential Equations and Linear Algebra ~$79.89 Used and ~$151.29 New. I am the least sure about this book in particular. But for a wag, I'm sure the numbers will work.
Calculus - Early Transcendentals ~$86.03 Used and ~$236.81 New.
So by my calculations your current "TV Stand" cost ~$1107.16. I'd recommend you go to amazon and sell the books you probably aren't ever going to crack the cover on again for ~$602.36 and buy yourself an actual TV stand with a little money left in your pocket.
I do all this because most of my friends in college complained about the costs of text books and then never sold them again. Or did the absolutely stupidest thing you could ever do with a book you've paid over $200 for and sold them back to the bookstore for ~$20 a pop. Don't be lazy, use amazon to sell your books back and the sting of your new found education won't be so bad. The idea is to get smarter right?
Sometimes you can find what textbook your school uses before the semester starts (I'm also the weird kid that emails the professor asking about books if I cant find it >.>). Some of my professors have what material they use for each class on their personal web pages though. For calculus, you'll most likely use this book. My brother used it at his Uni my friend at another and I myself used it at mine. Not sure if you're registered yet though. I had a weird case going into my Uni because I did community college then took summer courses so I was enrolled earlier than students who transfer and probably the freshman. YouTube videos will also be your best friend. People I liked for my math classes are TrevTutor (I don't think he ever finished his Calc 2 series) and PatrickJMT. Hope this helps a bit if you have any other questions or need more clarifications don't hesitate to ask.
This is what my school requires of us. https://www.amazon.com/gp/aw/d/1285740629/ref=mp_s_a_1_1?ie=UTF8&qid=1501294155&sr=8-1&pi=AC_SX236_SY340_FMwebp_QL65&keywords=calculus+stewart+8th+edition
Don't forget the $130 Web assign!
I recommend this book.
I would assume that if you're a music major and "been good at math", you might be referring to the math of high school. In any case, it would help if you spend some time doing/reviewing calculus in parallel while you go through some introductory physics book. So here's what you could do:
Other than that, feel free to google your question. You'll find good info on websites like physicsforums.com, physics.stackexchange.com, as well as past threads on this subreddit where others have asked similar questions.
Once you're past the intro (i.e., solid grasp of calculus, and solid grasp of mechanics, which could take up to a year), you are ready to venture further into math and physics territory. In that regard, I recommend you look at posts by Gerard 't Hooft and John Baez.
I did not spend $15,000 on algebra books, so I googled it. Turns out that, despite you and your uppity math skills, the stack of books is worth $12,402.56, or could be rented for a semester for $4,005--with free shipping!
Looks like someone got ripped off.
>..worth over $15,000.
BULLSHIT
I count 15 levels of 4 books. That's 60 books.(The OP reports there are 18 levels of books, making 72 books total. Figures corrected from my estimate of 60 books)
The book costs $193.79 new at Amazon.
$193.79 72 = Total price: $13952.88
BUT WAIT THERE'S MORE
Let's recalculate, using the Manufacturer's Suggested Retail Price of $206.
$206 72 = $14832
So even using the maximum price anyone would pay (MSRP) the value is well under $15000.
BUT WAIT THERE'S MORE
The OP reports the books cost $210 each. That price is well above MSRP. You would have to be an idiot to buy a college textbook at more than retail price.
Hawking is a theoretical physicist. His craft is closer to math than it is to classical physics.
You made a lot of erroneous and hot-headed statements, but that's understandable. Since you seem to be very, very ignorant of math, I don't even know where to even begin to show you the differences - I am at a disadvantage here :) How about we talk about levels, then?
Most math an engineer knows is barely a first year material for a math undergrad. Math is so vast that even the grad students of math are at the very base of a huge mountain.
Here's Basic Algebra for a math major(flip through the first pages and checkout the contents).
Here's Algebra for engineers.
Notice how the algebra for engineers is a very small part of general algebra and non-rigorous at that.
Here's Calculus for engineers.
Here's Calculus for math majors.
This is not to say engineers are mentally inferior to mathematicians, it's just these two professions are concerned with fundamentally different things.
lol thanks i'm furious.
btw, i have something for you:
http://www.amazon.com/Elementary-Algebra-Harold-R-Jacobs/dp/0716710471
don't thank me now. buy it read it fail to understand it realize you suck at math move on to something you're good at like raping/robbing/killing then come back and thank me for setting you on your proper life's path
> Turning in assignments should not be locked behind a pay wall. A student should not fail the class just because they didn't buy it.
You're not wrong, but I have a few issues with that.
First, do you really believe that the school does not have a system in place to help those that genuinely cannot afford it? Every class I've had that mentioned Cengage had the teacher explicitly mention that if paying for it was a problem, to get in contact with them.
As I mentioned, I used to go to a different school. $125 per semester, required by every math class I took. It's a good step down for me to pay that much in a year.
Second, we've got 750 students this semester in Calc 3 alone. I've got 3 assignments that were due yesterday, and 2 more due Monday.
If all the assignments only had 6 questions each, that's ~22k questions to be graded this week. Somebody has to do it. UCF is apparently even making their own software/site for this, but regardless of when it gets finished you know we're gonna foot the bill. One way or another we pay for this shit to get done.
> Also, access codes hurt the used textbook market.
You're not wrong but if we can get the textbook + assignments graded for the same price, what's the big deal?
Renting my textbook for Calculus would have cost the same as paying for access, and I covered both Physics classes too (along with whatever else I want to study on)
Beside the point either way. My issue was that the OP was full of shit, not 'Oh poor Cengage.' My bad for expecting people here to read instead of jumping in on another circlejerk.