∑📚 Math Resources – 🧮 andreas.hartel.me

Solutions to exercises from Introduction to Analytic Number Theory by Apostol

January 28th, 2023

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.

😳

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

February 6th, 2022

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. ⟨hal-03038776v3⟩

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

February 6th, 2022

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

January 30th, 2022

Great lecture notes on elementary number theory.

Link: http://math.bu.edu/people/jsweinst/Teaching/MA341Spring18/index.html

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. Morris

January 30th, 2022

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.

Math video lecture playlist: Complex Analysis by R. E. Borcherds

January 30th, 2022

Complex analysis video lecture playlist by R. E. Borcherds

Collecting free online resources for learning math

January 28th, 2022

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