Reddit reviews A Transition to Advanced Mathematics

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.

A Transition to Advanced Mathematics, I think

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 :)

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

• "I wonder how many different meals I can make at Chipotle" (like statistics, cryptography, AI, etc.) or,
  
• "I wonder how much faster this would be if we had two lines" (like queuing theory) or,
  
• "I wonder how they figure out the best time to order new Tabasco when it gets used up/stolen" (like optimization, inventory control),
  
  then you're closer to what math actually is.