Reddit reviews How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
We found 13 Reddit comments about How to Think Like a Mathematician: A Companion to Undergraduate Mathematics. Here are the top ones, ranked by their Reddit score.
Cambridge University Press
As someone just finishing their last year of Masters in maths undergrad, A lot of the stuff that you find in The Art of Problem Solving won't really show up until year 2 probably.
Here are the books I used in the summer before starting uni
"How to think like a Mathematician"
Bridging the Gap to University Mathematics
A Consise introduction to Pure Mathematics
Those books were interesting reads for me so I would recommend them. I'll answer any questions you have if you want.
Another good affordable recommendation is How To Think Like A Mathematician, which is aimed at people making the jump from school to university-level mathematics. It explains mathematical terminology and breaks down the process one might go through to read and write proofs.
I wish you good luck but also not to be demanding on yourself: learning to interpret and construct proofs, along with the required vocabulary, is about half (or more) of an undergraduate degree in mathematics, and some students never get the hang of it. The fact that you are actually motivated to understand proofs is a good start, though, and probably sets you apart from those students already. And of course, you have luxury of choosing which proofs interest you.
Feel free to pm me specific questions, I have a bit of free time this month until I'm back to my own studies. Can't promise I'll know the answer but if not can hopefully direct you somewhere useful.
Try one (or a few) of these:
http://www.amazon.ca/Thinking-Mathematically-J-Mason/dp/0201102382
http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X/
http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X
www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995/
www.amazon.com/Introduction-Mathematical-Thinking-Keith-Devlin/dp/0615653634/
https://www.coursera.org/course/maththink
I'm also planning on doing a Masters in Math or CS. What do you plan to write for your masters?
> Anybody else feels like this?
I think its natural to doubt yourself, sometimes. I dont know what else to say, but just try to be objective and emotionless about it (when you get stuck in a problem).
The following books that helped me improve my math problem solving skills when I was an undergrad:
You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.
Some user friendly books on Real Analysis:
Some user friendly books on Linear/Abstract Algebra:
Topology(even high school students can manage the first two titles):
Some transitional books:
Plus many more- just scour your local library and the internet.
Good Luck, Dude/Dudette.
Polya's How to Solve it is a classic.
You might prefer Housten's How to Think Like a Mathematician which is much more modern.
I found that they both had useful insights, though there was a fair bit of information which I didn't find helpful.
Try the "for dummies" books (for real). I went to a top ten uni for maths and didnt really go to my calculus lectures (they were monday and tuesday mornings). I went through "differential equasions for dummies" and it got me a high 2:1. Plus, they are loads cheaper than most other text books.
Also, this book is good for general. "How to think like a mathematician" - http://www.amazon.co.uk/How-Think-Like-Mathematician-Undergraduate/dp/052171978X
Got it!
Well you have a couple of routes. You can choose to go the traditional route of learning mathematics. That is the following:
Trigonometry
Calculus (Derivatives, Integrals, Series, then Multivariable)
Differential Equations
Linear Algebra
After linear algebra you branch off from there.
If you want a non-traditional approach, you can start by understanding logic. This will really help fortify the way you should think about math. Picking up books on logic is great for this. /r/bibliographies is a great place for this. You should find the logic or philosophy section and dip your feet in it (More specifically the symbolic logic section). I would take a look at those books. If anything, I would try to check out the book How To Think Like a Mathematician. It is a pretty good book. What is best about it is that the ideas of logic is explained with set theory.
Set theory is the next math I would learn after logic. It is a building block of mathematics and quite fun (though proof heavy). I wouldn't be surprised if this even turned you away! I would just try this and just try very elementary set theory.
There's books that might help, or google "college math study guide" or read soft questions at math.stackexchange but there aren't any secret hacks/Royal Road, you have to skim a lot of books/lecture notes/videos to select a few you work intensively, network with motivated students, good diet/sleep/exercise habits etc
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Here's a few weeks of reading:
https://www.google.com/search?q=site%3Anews.ycombinator.com%2F++college+math+study+guide&ie=utf-8&oe=utf-8
http://www.math.utah.edu/~pa/math.html
https://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X
Introduction to Mathematical Thinking, Keith Devlin
Cal Newport Deep work
Study as a Mathematics Major Lara Alcock
Here's my radical idea that might feel over-the-top and some here might disagree but I feel strongly about it:
In order to be a grad student in any 'mathematical science', it's highly recommended (by me) that you have the mathematical maturity of a graduated math major. That also means you have to think of yourself as two people, a mathematician, and a mathematical-scientist (machine-learner in your case).
AFAICT, your weekends, winter break and next summer are jam-packed if you prefer self-study. Or if you prefer classes then you get things done in fall, and spring.
Step 0 (prereqs): You should be comfortable with high-school math, plus calculus. Keep a calculus text handy (Stewart, old edition okay, or Thomas-Finney 9th edition) and read it, and solve some problem sets, if you need to review.
Step 0b: when you're doing this, forget about machine learning, and don't rush through this stuff. If you get stuck, seek help/discussion instead of moving on (I mean move on, attempt other problems, but don't forget to get unstuck). As a reminder, math is learnt by doing, not just reading. Resources:
math on irc.freenode.net
Here are two possible routes, one minimal, one less-minimal:
Minimal
Less-minimal:
NOTE: this is pure math. I'm not aware of what additional material you'd need for machine-learning/statistical math. Therefore I'd suggest to skip the less-minimal route.
sounds wonderful! ill add that to the list. i was also thinking of 'how to think like a mathematician: a companion to undergraduate mathematics' - kevin houston. from the amazon 'look inside' i'm following pretty well
don't know if you've seen it before but does it look alright?
I really like this book on proofs.
I wasn't a math major, but I enjoyed this book:
http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/052171978X