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u/proffrobot · 1 pointr/AskPhysics

It's great that you want to study particle physics and String Theory! It's a really interesting subject. Getting a degree in physics can often make you a useful person so long as you make sure you get some transferable skills (like programming and whatnot). I'll reiterate the standard advice for going further in physics, and in particular in theoretical physics, in the hope that you will take it to heart. Only go into theoretical physics if you really enjoy it. Do it for no other reason. If you want to become a professor, there are other areas of physics which are far easier to accomplish that in. If you want to be famous, become an actor or a writer or go into science communication and become the new Bill Nye. I'm not saying the only reason to do it is if you're obsessed with it, but you've got to really enjoy it and find it fulfilling for it's own sake as the likelihood of becoming a professor in it is so slim. Then, if your academic dreams don't work out, you won't regret the time you spent, and you'll always have the drive to keep learning and doing more, whatever happens to you academically.

With that out of the way, the biggest chunk of learning you'll do as a theorist is math. A decent book (which I used in my undergraduate degree) which covers the majority of the math you need to understand basic physics, e.g. Classical Mechanics, Quantum Mechanics, Special Relativity, Thermodynamics, Statistical Mechanics and Electromagnetism. Is this guy: Maths It's not a textbook you can read cover to cover, but it's a really good reference, and undoubtably, should you go and do a physics degree, you'll end up owning something like it. If you like maths now and want to learn more of it, then it's a good book to do it with.

The rest of the books I'll recommend to you have a minimal number of equations, but explain a lot of concepts and other interesting goodies. To really understand the subjects you need textbooks, but you need the math to understand them first and it's unlikely you're there yet. If you want textbook suggestions let me know, but if you haven't read the books below they're good anyway.

First, particle physics. This book Deep Down Things is a really great book about the history and ideas behind modern particles physics and the standard model. I can't recommend it enough.

Next, General Relativity. If you're interested in String Theory you're going to need to become an expert in General Relativity. This book: General Relativity from A to B explains the ideas behind GR without a lot of math, but it does so in a precise way. It's a really good book.

Next, Quantum Mechanics. This book: In Search of Schrodinger's Cat is a great introduction to the people and ideas of Quantum Mechanics. I like it a lot.

For general physics knowledge. Lots of people really like the
Feynman Lectures They cover everything and so have quite a bit of math in them. As a taster you can get a couple of books: Six Easy Pieces and Six Not So Easy Pieces, though the not so easy pieces are a bit more mathematically minded.

Now I'll take the opportunity to recommend my own pet favourite book. The Road to Reality. Roger Penrose wrote this to prove that anyone could understand all of theoretical physics, as such it's one of the hardest books you can read, but it is fascinating and tells you about concepts all the way up to String Theory. If you've got time to think and work on the exercises I found it well worth the time. All the math that's needed is explained in the book, which is good, but it's certainly not easy!

Lastly, for understanding more of the ideas which underlie theoretical physics, this is a good book: Philsophy of Physics: Space and Time It's not the best, but the ideas behind theoretical physics thought are important and this is an interesting and subtle book. I'd put it last on the reading list though.

Anyway, I hope that helps, keep learning about physics and asking questions! If there's anything else you want to know, feel free to ask.

u/MetalMagnum · 4 pointsr/AskPhysics

Hiya! I'm a recent physics/computer science graduate and although I can't think of any super cool handmade options off the top of my head, there are some physics books that I find interesting that your boyfriend may enjoy. One solid idea would be just about anything written by Richard Feynman. Reading through the Feynman Lectures is pretty standard for all physicists, though there are free versions online as well. There are a few others, such as The Pleasure of Finding things Out and Surely You're Joking Mr. Feynman. There's also a cool graphic novel that recounts the events of his life called Feynman by Ottaviani. If you're not familiar with who this guy is, he is a colorful and concise orator who won a nobel prize in physics. His biggest contributions were in nuclear physics and quantum computation, and his quirks make his explanations of these topics very interesting. The Feynman Lectures are more formal, while his personal books are a mixture of personal experience and explanation.

Something else that I typically gift all of my friends who are problem solvers interested in physics is the book Thinking Physics. This book is great for developing some high level intuition in every field of physics (mechanics, optics, thermodynamics, electricity and magnetism, quantum mechanics, etc.). This book is great because it's broken into small digestible sections that build your knowledge as you solve more of the questions (solutions are given).

Good luck!

u/MahatmaGandalf · 2 pointsr/AskPhysics

You sound like a great audience for the series I recommend to everyone in your position: Lenny Susskind's Theoretical Minimum. He's got free lectures and accompanying books which are designed with the sole purpose of getting you from zero to sixty as fast as possible. I'm sure others will have valuable suggestions, but that's mine.

The series is designed for people who took some math classes in college, and maybe an intro physics class, but never had the chance to go further. However, it does assume that you are comfortable with calculus, and more doesn't hurt. What's your math background like?

As to the LHC and other bleeding-edge physics: unfortunately, this stuff takes a lot of investment to really get at, if you want to be at the level where you can do the actual derivations—well beyond where an undergrad quantum course would land you. If you're okay with a more heuristic picture, you could read popular-science books on particle physics and combine that with a more quantitative experience from other sources.

But if you are thinking of doing this over a very long period of time, I would suggest that you could pretty easily attain an advanced-undergraduate understanding of particle physics through self-study—enough to do some calculations, though the actual how and why may not be apparent. If you're willing to put in a little cash and more than a little time for this project, here's what I suggest:

  • Pick up a book on introductory physics (with calculus). It doesn't really matter which. Make sure you're good with the basic concepts—force, momentum, energy, work, etc.

  • Learn special relativity. It does not take too long, and is not math-intensive, but it can be very confusing. There are lots of ways to do it—lots of online sources too. My favorite book for introductory SR is this one.

  • Use a book or online resources to become familiar with the basics (just the basics) of differential equations and linear algebra. It sounds more scary than it is.

  • Get a copy of Griffiths' books on quantum mechanics and particle physics. These are undergrad-level textbooks, but pretty accessible! Read the quantum book first—and do at least a few exercises—and then you should be able to get a whole lot out of reading the particle physics book.

    Note that this is sort of the fastest way to get into particle physics. If you want to take this route, you should still be prepared to spread it out over a couple years—and it will leave a whole smattering of gaps in your knowledge. But hey, if you enjoy it, you could legitimately come to understand a lot about the universe through self-study!
u/HQuez · 2 pointsr/AskPhysics

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!

u/thebenson · 3 pointsr/AskPhysics

I think you posted something similar in the math thread right? Introductory physics is really just math and being able to plug into formulas. I'd say it'd be best to get a good math foundation before tackling physics (especially calculus). As far as book recommendations ... I Googled and found a very comprehensive list (

There should be tons of stuff on Khan Academy or on YouTube for particular subjects. Sometimes this may be even more useful than just studying a book as both math and physics books can be dense. I guess I should just list the books I have. Maybe you'll find them useful. I'll list my physics and math books separately.

In general, the Feynmann lectures are considered to be like the physics bible. You can buy a hardcover boxed set of these lectures here: Be forewarned that the lectures were intended for physics students, so it may be best to read a general physics textbook first.

Math (in no particular order):

-Advanced Engineering Mathematics by Greenberg

-Calculus: Early Transcendentals Multivariable by James and Stewart

-Thomas' Calculus Early Transcendentals (Single Variable) by Weir and Hass

-Linear Algebra and its Applications by Lay

-Differential Equations: Computing and Modeling by Edwards and Penney

-Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni and Zhang

-A First Course in Partial Differential Equations with Complex Variables and Transform Methods by Weinberger

Physics (in no particular order):

-Intro to Quantum Mechanics by Griffiths

-University Physics by Young and Freedman (prob a good starting place)

-Spacetime Physics by Taylor and Wheeler

-Analytical Mechanics by Fowles and Cassiday

-Fundamentals of Physics by Halliday, Resnick and Walker

-Intro to Electrodynamics by Griffiths

-Heat and Thermodynamics by Zemansky and Dittman

-Statistical and Thermal Physics by Gould and Tobochnik

I hope this was helpful! If not, the physics subreddit has a dedicated thread each week to learning materials and I'm sure someone over there would be glad to help you.

u/v3nturetheworld · 1 pointr/AskPhysics

Awesome! I recommend taking whatever physics classes your High School offers along with as much math as possible. I also suggest taking advantage of the website Kahn Acadamy. Another good site for asking questions and learning more is it's very active and you can learn a lot there. For keeping up with physics and science, I like the site

A good book I would suggest starting with, while non-technical, but is an interesting read is Surely You're Joking Mr. Feynmann. Another good resource is the Feynmann Lectures on Physics, you can read them for free online now here:

And another awesome resource would be the Physics teachers at your school. Talk to them about what your interested in and they might be able to talk to you more about it!

If your high school doesn't have what your looking for you could also look into taking classes at your local community college as well.

u/tikael · 1 pointr/AskPhysics

What level E&M? If it is intro physics 2 then look for AP physics B/C stuff in addition to what you would normally look for since that's the same level.

If it is an upper division E&M class then I will recommend a book you can probably find in most of your professors offices somewhere: Div, Grad, Curl, and All That. Older editions are much cheaper even and has a PDf of the 3rd edition. I have no idea what the differences are, but I have the 4th and it is just great.

I have yet to find an E&M textbook I like. Griffiths is alright and when paired with Div, Grad, Curl and maybe a Schaum's outline on E&M it forms what I think should just be one textbook.

As for online resources I think The Mechanical Universe about Maxwell does a great job at covering Maxwell's laws, especially the bit starting around 15 minutes in

I've never used this site but it looks like it has a bunch of solved problems as well.

u/Rapturehelmet · 2 pointsr/AskPhysics

All the video sources I'm finding seem... spotty, but Richard Feynman's lectures on physics are the best in my opinion. He starts out with the basic foundations modern physics and progresses into much more difficult territory. They're well written, and definitely a good read for anyone who wants a basic understanding of physics.

I have these copies of his lectures which I like because they split up the easy and the hard topics in to separate books. But this is just personal opinion, and there are many, many copies of his works out there.

u/nodayzero · 3 pointsr/AskPhysics

I got the new millennium edition. While I was researching which one to get , a lot of people mentioned that millenium edition was glossy and had smaller print which made it harder to read. I must say it looks fine. I don't have any problems so far. The reason i picked the latest is because it was relatively cheaper (140ish vs 300+) and had over 900 erratas fixed with respect to older editions.

Bonus: Another book I started reading in tandem is Road to Reality by Penrose which is equivalent in excitement, inspiration and quality of material and gives a nice overview of math required for physics and relation between math and physics. Highly recommend.

u/bodieskate · 2 pointsr/AskPhysics

When I first got interested in physics and before I developed the mathematical framework, someone directed me towards this book. It's great because it assumes (as far as I can remember) no real mathematical background, yet delves into the concepts very intuitively. It still sits on my shelf next to my more "serious" books. Love that book.

Side note: You should give a little bit of your background (read: mathematics) so we can better help you out.

u/Tobiasuru · 8 pointsr/AskPhysics

An Introduction to Thermal Physics

This is the standard undergraduate text. It's the one I used. Super easy to read and the problems are fun. Best of luck!

u/cdbradley · 2 pointsr/AskPhysics

If your goal is to understand basic concepts without the math, then a highschool physics book would most likely be the best place to start, as the highest math used is usually Algebra/Pre-calc.

That being said, without at least a calculus background it's hard to grasp some of the concepts beyond basic kinematics. Wikipedia might get you somewhere so it's a good place to start, but it could also lead you through a rabbit hole to pages upon pages of background.

I'd say if you want to tackle more advanced physics concepts then you need at least some background in math, so I'd try Mathematical Methods in the Physical Sciences by Mary Boas, a book that explains the physics and math somewhat side by side, or The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose. Neither is a light read, if you don't have a head for math don't even try Penrose as he uses arguments that assume a reasonable mathematical background. The Boas book is technically a mathematics textbook, so you would do well to supplement it with a College Physics textbook (I used one by Tipler in my university courses).

Amazon Links Below:



Hope this helps, good luck!

u/dawiseguy98 · 1 pointr/AskPhysics

In a similar vein, I really enjoyed Surely You're Joking Mr. Feynman.

It's an autobiography of Fenyman's shenanigans. Lighter on the physics, but if he's a Feynman fan, he'll love it.

u/Merccii · 2 pointsr/AskPhysics

I guess this one?

However, as someone in the review states that:
> I wish I had read the original book instead of this one, or at least read it first.

I'm wondering: did you read the first book and can you maybe explain me which one would be a better read?

EDIT: Also, which book does the person in the review refer to?
Im sorry, I'm stupid. Amazon itself states that:
> hugely successful Mr Tompkins in Paperback (by George Gamow) in 1965.

Anyway, my question still stands: have you read both and can you recommend me one?

u/InfanticideAquifer · 2 pointsr/AskPhysics

Feynman's book on QED is supposed to be great (I haven't read it). But it will in no way help you with an undergraduate QM course. (Or with most graduate courses for that matter.) QED is the quantum field theory that governs the interactions of light and electrons; it's the most accurately tested theory ever written down, and it's awesome. But it is not covered in a standard QM course, and the things he talks about (path integrals) that could be used to do "regular" QM aren't actually used at all in most courses.

For a first introduction to QM, I used Griffiths. I don't think it was great, but I don't have any complaints. Someone else linked Shankar, which is usually considered to be a graduate level text.

The third volume of the Feyman Lectures covers quantum mechanics. It takes a less mathematical, more physical approach--very grounded in experiment. I've heard people say that it's a nice complement to the traditional textbooks.

u/Dank_Hamiltonian · 2 pointsr/AskPhysics

First and foremost, you're going to need to get very comfortable with special relativity and quantum mechanics. QFT is heavily rooted in both subjects since it's essentially a way of reconciling the two, so you're going to need to get familiar with the formalism. For quantum mechanics, I recommend starting off with Griffiths if you haven't taken a class on the subject at an undergraduate level. It's pretty much the gold standard in undergraduate physics curricula. But that alone is not enough to fulfill the necessary background in quantum. After that you'll want to go through a graduate text such as Sakurai. You need to get very familiar with the Dirac formalism since it plays a large role in formulating quantum fields.

Special relativity isn't usually offered as a course on its own in most universities (as far as I know). Typically, it's part of a course on classical dynamics or electrodynamics. You could look for the relevant chapters in textbooks on those two subjects (such as Griffiths electrodynamics) or just go with the introduction that pretty much every QFT textbook has at the beginning. The main thing here is that you'll have to get used to working with tensors since they show up in Lagrangian densities, which are principal objects of study in QFT. This is also where classical field theory comes in, as classical fields are also described by Lagrangians.

Those are the main areas of physics that you need to know coming into the subject. As others have mentioned, you'll want to understand Hamiltonian and Lagrangian mechanics as well as classical E&M since a lot of the formalism involved in QFT stems from those subjects. Most people are introduced to quantum through the Hamiltonian formalism, and while you can do calculations in quantum without understanding where the formalism comes from in classical mechanics, you might be confused as to why the calculations work the way they do. You can also do calculations with a Lagrangian in QFT without really understanding what actually is, but again, if you truly want to understand the material it won't get you quite far enough. It is a graduate subject, after all. So you'll probably struggle to understand the material without having a solid undergraduate background in physics, but it's not impossible. It's also the kind of subject that requires multiple attempts to understand it. I took one semester of it as an undergraduate and there were a lot of gaps in my knowledge at the time, so I found it quite difficult. Then I took another class on it again after going through first year graduate courses in classical mechanics, quantum, and electrodynamics, and I had a better feel for the subject.

u/wupdup · 1 pointr/AskPhysics

Enjoy the course! I'm an amateur with an interest in relativity. Most tests of GR are tests of the Schwarzschild metric. Check out Orbits in Strongly Curved Spacetime. The BASIC code for plotting orbits in Schwarzschild geometry is the 2nd link in the 1st reference. Also I highly recommend the books Exploring Black Holes and Relativity Visualized.

u/The_Serious_Account · 2 pointsr/AskPhysics

Max Tegmark likes to engage in these slightly fringy topics. As I understand he does standard work in physics and occasionally go into areas like this. It's highly speculative, but, as far as I can tell, his reasoning is generally pretty solid.

In terms of additional evidence for (or against) such a universe, I think your best bet is to look at the anthropic principle. Sean Carroll in his book From Eternity to Here: The Quest for the Ultimate Theory of Time discusses an alternative theory that Boltzmann had and I think his objections might apply here. In the most extreme sense of Tegmark's argument every cubic meter of space is in a random state and by simple chance of an infinite universe one of those cubic meters are going to contain "you". This is similar to Boltzmann's view where our universe was a low entropy fluctuation of an infinite universe in thermal equilibrium (of course, now we know of the big bang and our view of the history of the universe is very different). The counterargument to such a universe is that of so-called Boltzmann brains.

If, indeed, the universe contains an infinite number of cubic meters and an infinite number of "you"s, the question you might ask yourself is what universe you should see around you? The vast majority of "you"s would see nothing. There is so much structure around you, other humans, planets, stars, galaxies, etc that the idea that you're a result a random state in the universe is extremely problematic.

u/isentr0pic · 2 pointsr/AskPhysics

Interdisciplinary connections spring up from generality. You'd be hard pressed to find a spontaneous connection between something like particle phenomenology and an unrelated field.

To illustrate this idea of generality, consider the methods of statistical mechanics, which are so general that they can be used to describe everything from black holes to ferromagnets. However, the methods have also been used to model neural networks and social dynamics (the latter being accurate enough to successfully recreate historical events.)

What makes statistical mechanics more general than other branches? Probably the fact that it's almost more mathematics than physics, specifically a branch of probability theory regarding highly correlated random variables.

With this in mind, perhaps you'd benefit from focusing your attention on the mathematical ideas that drive physics rather than physics itself. Take the calculus of variations which, whilst developed for problems in classical mechanics, has found applications in mathematical optimisation. Another example being brownian motion, the mathematics of which have been generalised to higher dimensions and applied to finance. The mathematics behind relativity is differential geometry, which has been applied to too many fields to list.

I'd recommend having a look at Mathematical Methods for Physicists by Arfken, Weber and Harris for a broad overview of the methods.

u/vakini · 1 pointr/AskPhysics

I need more info regarding his level of knowledge. As someone who went through the same struggles that this student is going through, I can recommend a lot of books but it depends on how much they know. In terms of cheaper books, If they've completed 18.01-18.03 and 18.06 plus 8.01-8.04 then the book "Road to Reality" by Roger Penrose is a good option. It's a huge book so it should keep him busy for a while and gives a very comprehensive treatment of various topics in mathematical physics.
here's the link:

u/stankind · 2 pointsr/AskPhysics

Epstein also has a great book called Relativity Visualized that goes great with Thinking Physics.

u/[deleted] · 1 pointr/AskPhysics

Special relativity tells us it couldn't work. That theory is very well tested in labs, so we have good reason to believe it's valid. I think with your curiosity you'd like the book Relativity Visualized. There are few equations. Mostly the author appeals to your intuition. You'd gain an excellent understanding of relativity.

The theory tells us that the speed of accelerating objects (e.g. particles in a particle accelerator) can ever more closely approach but never reach the speed of light.

u/South_Dakota_Boy · 2 pointsr/AskPhysics

Griffiths Electrodynamics would be a good thing to look at. It's surprisingly readable, and it could possibly wind up being your E&M textbook. In my undergrad, E&M was the "weed out" course, where those who weren't up to scratch lost interest in the physics degree, so it's good to get a head start. I wish I had started on it sooner. Maybe I'd have gotten more out of E&M as an undergrad and then Jackson in grad school wouldn't have been so hard.

u/DrunkenPhysicist · 1 pointr/AskPhysics

Griffith's Electrodynamics has a decent introduction to special relativity. Otherwise, Hartle's book is geared towards the advanced undergrad. Also, Schultz is good too.

u/this_is_real_armour · 1 pointr/AskPhysics

To be honest it's really hard to learn without doing the coursework. But yes such books exist; for example You'll have to supplement with other things, but that should be a good backbone. There is also this list:

u/jeampz · 3 pointsr/AskPhysics

Feynman. Anything you can find on him. "The Feynman Lectures on Physics" is a brilliant introduction. It is aimed at college level but there's a significant portion of general audience material. A book was written that is a subset of the Feynman lectures that concentrates on the non-mathematical (which apparently means "easy") parts.

Edit: Okay, perhaps not anything you can find.

u/razzafrazzin · 1 pointr/AskPhysics

How to Teach Relativity to Your Dog is a good one that explains the concepts by less abstract analogies. You might like it:

u/starkeffect · 1 pointr/AskPhysics

You should probably start by cracking open a copy of a good E&M book, like this one, and learning the science, rather than relying on Einstein quotations.

Of course, that assumes you've already learned integral and differential calculus (which any 19-year-old science or engineering student has).

u/drzowie · 2 pointsr/AskPhysics

Mr. Tompkins in Paperback is exactly her speed. It's by George Gamow with a posthumous second edition. Explores modern physics through a series of short-stories involving a pudgy British banker (Mr. Tompkins himself). Mr. Tompkins keeps falling into alternate universes where the physical constants are macroscopic (e.g. 10m/s for c, or 1 J•s for h). Great for building intuition and wonder.

u/mini_fast_car · 3 pointsr/AskPhysics

You might want to look at this book. It's high level enough and Feynman does a good job explaining it.

u/astrolabe · 2 pointsr/AskPhysics

I learned the basics from Shutz (which I liked a lot). I don't remember it requiring Lagrangian/Hamiltonian stuff.

u/McVomit · 3 pointsr/AskPhysics

The book is Mr. Tompkins in Wonderland.

If I had to make my own suggestion for a book, it would be How to Teach Relativity to Your Dog. Each chapter starts off as a conversation between the author and his dog, where the dog has heard some random fact about physics and is trying to exploit it for her own gains(catching squirrels, infinite bacon, etc..). Then the second part of each chapter is a more rigorous(but still easy to follow) mathematical explanation.

u/totallynotshilling · 2 pointsr/AskPhysics

Haven't used it myself, but you might want to check out Div,Grad,Curl by Schey.

u/mjanmohammad · 1 pointr/AskPhysics

We used this book in my intro level physics lab for error analysis.

u/xrelaht · 5 pointsr/AskPhysics

This should keep you busy, but I can suggest books in other areas if you want.

Math books:
Linear algebra:
Linear algebra:

Beginning physics:

Advanced stuff, if you make it through the beginning books:

Cosmology -- these are both low level and low math, and you can probably handle them now:

u/listens_to_galaxies · 3 pointsr/AskPhysics

The idea of significant figures is a simplification of error analysis. It doesn't produce perfect results, as you've found in your example. It's useful as a simple rule of thumb, especially for students, but any proper analysis would use real error analysis. Your approach of looking at the range of possible values is good, and is basically the next level of complexity after sig figs.

The problem with error analysis is that it's a bit of a bottomless rabbit-hole in terms of complexity: you can make things very complicated very quickly if you try to do things as accurately as possible (for example: the extreme values in your range of possible times are less likely than the central values, and since your using the inverse of the time, that produces a non-uniform distribution in the velocities. Computing the actual probability distribution is a proper pain in the ass).

My advice is this: if you're a highschool student or non-physics university student, stick to sig-figs: it's not perfect, but it's good enough for the sorts of problems you'll be working with. If you're a physics major, you should learn some basic error analysis from your lab courses. If you're really interested in learning to do it properly, I think the most common textbook is the 'Introduction to Error Analysis' by Taylor.