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1 point

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2nd Dec 2020

I would recommend A Transition To Advanced Mathematics by Douglas Smith if you want to learn about proofs and set theory. I think the book is laid out very well, however, there is a ton of typos in the book. I'm not really sure how this ends up happening, but I've gone through this whole thing and rest assured if you are completely not understanding how the hell they go from one thing to the next then it's most likely a typo. Despite that the book does a very good overview. There are even some pages dedicated on how to write proofs formally and all of the rules you must follow.

I think the chapter on Cardinality is one of the coolest chapters in the book. It's really interesting especially when you are looking at infinite sets and the difference between countable and uncountable infinite sets. Also the sections on the ordering of sets are extremely interesting. Especially the proof of existence of infinite sets with different cardinalities( meaning the cardinality of the interval (0,1) is a bigger infinity than all real numbers). It's a short proof but it's probably the most genius thing ever written.

The book is written in a way as if you're building the foundations of Math from scratch. So it introduces you to a topic then proves those things based off of everything you learn so far. Some topics it will introduce but you "haven't learned enough" yet to prove it. Very cool book. It's like $30 for a used hard copy on amazon if you want the previous edition.

1 point

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12th Jul 2020

I took a class in college called Principles of Mathematics whose sole purpose was to prepare you for those more advanced, proof based math classes and not the computation based ones. The textbook we used was this one. I highly highly recommend at least the first 4 chapters of that book as it describes the necessity and methodology of proving things, which is necessary to make sense of why some proofs are approached a certain way.

2 points

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17th Oct 2018

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).

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.

^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.

$200 - $300

< $50

$200 - $300