The Best Books for Algebraic Topology

Algebraic Topology: A First Course

This is a good book if you have some prior knowledge in the subject. So if you have already read a bit about the subject and want to learn more, buy it. The author appears to know how to position material to make it interesting to on board a reader but it can a bit long winded and abstract towards the end.

A Concise Course in Algebraic Topology

Like the above, only a basic introduction to algebraic topology is needed to get started with this book. Check for the version or edition of the book, and buy the latest one. The book has some typos which will be corrected in the latest version. The homework problems in the book can get very demanding.

Algebraic Topology

See this book as a go-between undergraduate and graduate levels for the subject. The book starts off well by giving an overview and introduction to topology but gets complex towards the later chapters.

Algebraic Topology 1st Edition

Think carefully before you buy this book, because it requires strong background knowledge in the subject before you read it. This is not an introductory book. After buying this book, you will invariably come away either liking or disliking it rather strongly.

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The Best Books to Learn Probability

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Fun with Uniform Random Numbers

Q: You have two uniformly random numbers x and y (meaning they can take any value between 0 and 1 with equal probability). What distribution does the sum of these two random numbers follow? What is the probability that their product is less than 0.5. The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists A: Let z = x + y be the random variable whose distribution we want. Clearly z runs from 0 to 2. Let 'f' denote the uniform random distribution between [0,1]. An important point to understand is that f has a fixed value of 1 when x runs from 0 to 1 and its 0 otherwise. So the probability density for z, call it P(z) at any point is the product of f(y) and f(z-y), where y runs from 0 to 1. However in that range f(y) is equal to 1. So the above equation becomes From here on, it gets a bit tricky. Notice that the integral is a function of z. Let us take a look at how else we can simply the above integral. It is easy to see that f(z-y) = 1 when (

Probability Puzzles

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