Category: âˆ‘ðŸ“š Math Resources

• Solutions to exercises from Introduction to Analytic Number Theory by Apostol

As I am currently working my way through the exercises in Apostol’s book “Introduction to Analytic Number Theory”. Since I wasn’t able to find solutions to all exercises and since the book does not contain solutions, I googled for them.

And then I found this: https://gregoryhurst.com/solutions/. A PDF file containing solutions to most if not all exercises in the book.

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Since graduating, I decided to work out all solutions to keep my mind sharp and act as a refresher.

Greg Hurst, author of the solutions, in its preface

I was very happy to have found this work and I am very thankful to its author!

• Free lecture notes: Statistics and Machine Learning in Python

These lecture notes were sent to me by a friend and I thought why not add them to my collection. The notes are available as a browsable website (https://duchesnay.github.io/pystatsml/) as well as a PDF (https://raw.github.com/duchesnay/data/master/pdf/StatisticsMachineLearningPython.pdf). They also come with exercises, some of which even come with prepared jupyter notebooks.

I guess the “official” way to cite the book in a scientific publication is this way:

Edouard Duchesnay, Tommy Lofstedt, Feki Younes. Statistics and Machine Learning in Python. Engineering school. France. 2021.Â âŸ¨hal-03038776v3âŸ©

• Free math lecture notes: Irrational and transcendental numbers by Michel Waldschmidt

I only recently found out that it is an open question whether the Euler-Mascheroni constant is irrational or not and whether is transcendental or not. I found that quite surprising and looked for lecture notes on the topic. I found these lectures by Michel Waldschmidt with the title: “An introduction to irrationality and transcendence methods.”:

There is also a series of video lectures by the same author on Youtube:

The title image of this post is by Arthur Baelde on Wikimedia Commons. See https://commons.wikimedia.org/wiki/File:First_irrational_numbers.svg

• Free math lecture notes: Number theory by Jared Weinstein

Great lecture notes on elementary number theory.

Very clear and gentle introduction to number theory by Jared Weinstein. These lecture notes really start off the ground and explain number theory in a gentle and clear way.

• Free math text book: Topology without tears by Sidney A. Morrisï¿¼

Link to the homepage of the book: https://www.topologywithouttears.net/

A PDF version of the book can be downloaded for free from the above website. It contains lots of exercises, but without solutions. I did go through chapters 1 and 2 and I found it clear and well readable with lots of examples.

• Collecting free online resources for learning math

Inspired by a recent video on self-study math videos and books by Aleph 0 and by the website libraryofbabel.info (which I found via this tweet) I decided to collect all online resources (text books, playlists, websites) for learning undergraduate and graduate math online that I know of. This collection will hopefully grow over the next weeks and months.

I decided to list each individual text book and Youtube playlist on a certain topic individually rather than only listing, for example, the Youtube channel that contains them or the author’s homepage, in case an author has more than one text book online. I think this makes the list more searchable and (probably?) of higher quality.

I hope that the list will be helpful to someone. Here’s the link to the blog category that I’ll use to file the posts: Math-resources

• Math video lecture playlist: Group Theory from Harvard

Lectures on Group Theory by Benedict Gross of Harvard.

Found via the Self-study guide by Aleph 0.