Math Resources

It's time to start your Math Journey

Wherever you are, wherever you’re going, there are some resources here for you, from books to websites to video series. This page is updated regularly, so make sure to check back frequently to see what gets added.

Guides

Whether it is figuring out what material to cover for a particular topic or deciding on your broader goals, here are some guides to help you out:

Textbooks

You cannot learn mathematics without some quality textbooks to learn it from. (Note: I provided a link to the Amazon page for each book, but I do receive not any compensation for purchases. The links are solely for your convenience.)

  • A Book of Abstract Algebra by Charles Pinter: (Amazon) This is truly the book that ignited my passion for math. It is the perfect starting point for getting into higher math. My main complaint is the lack of solutions for many of the exercises.
  • How to Prove it: A Structured Approach by Daniel Velleman: (Amazon) (Also available online) This is a commonly recommended book from which to learn proofs. The book is challenging but thorough. 
  • r/math has a huge list of book recommendations. 
  • Mathematical Association of America Book Reviews: This is a searchable list of over thirteen thousand math books, most of them with reviews.
  • European Mathematical Society Book Reviews: Several hundred more book reviews.
  • Mathematics Subject Classification: This is essentially like the Library of Congress Classification system, except that it is specifically for mathematics. 

Fun Books

When you are looking for some lighter mathematical reading (or something younger math enthusiasts) there are plenty of options to choose from. Here are a some of my favorite popular math books. (Note: I provided a link to the Amazon page for each book, but I do receive not any compensation for purchases. The links are solely for your convenience.)

  • How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg: (Amazon) I enjoyed reading this book. The writing style is playful and there are many stories/real world connections weaved into the content. The book focuses on thinking mathematically in oder to avoid some of the mental pitfalls that it is all too easy to fall into. 
  • In Pursuit of the Unknown: 17 Equations That Changed the World by Ian Stewart: (Amazon) Like the title says, this book discusses 17 different and their impact on the world. For each equation, Stewart presents the history of the problem, how the equation works, and how it is used in the world. It makes for a nice tour of mathematics.
  •  The Joy of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz: (Amazon) This book starts from the notion of counting and builds up from there. Strogatz has a way of writing that is both entertaining and informative. Despite being a purposefully accessible book, The Joy of X gets into some wonderfully interesting and applicable mathematics such as Markov Chains (specifically how the PageRank algorithm works). Honestly, my only complaint about this book was that it build up my excitement so high and then had the audacity to end.  
  • Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire: (Amazon) I love this book. It is a lively history of specifically algebra (including linear and abstract algebra). The author alternates between chapters which intuitively explain the topics under discussion and chapters which focus on the historical events and figures involved.
  • Prime Obsession: Bernhard Riemann and the greatest Unsolved Problem in Mathematics by John Derbyshire: (Amazon) Another book by Derbyshire, this one reads like a mystery novel. Each chapter reveals a new piece of the puzzle, building the suspense until the full impact of the Riemann Hypothesis is revealed towards the end of the book.
  • The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall: (Amazon) Once I picked this book up, I couldn’t put it down. I believe I finished it the same day I got it. This book explores the math and physics concepts which have come to dominate the financial markets. There was a surprising amount of interplay between math, physics, and finance which I was not really aware of until I read this book.
  • Calculating the Cosmos: How mathematics Unveils the Universe by Ian Stewart: (Amazon) This book is a celebration but also a warning. The book explains and celebrates how we have used the power of mathematics to better understand the universe and out place within it. However, the book ends with a warning about not being blinded by the math, and keeping our feet planted firmly in reality even while our heads soar through the heights of theory.
  • American Mathematical Society’s Math in the Media: This page has a large collection of reviews for math related books, plays and films. The focus is on media which is accessible to a more general audience. 

Videos/Channels

Sometimes it doesn’t matter how good a textbook is and you just need to see and here someone explain a concept. That is where video resources come in handy. 

  • 3Blue1Brown: By far my favorite math YouTuber, every video on this channel is amazing. In particular, his essence of linear algebra and essence of calculus series are wonderful supplements when studying those topics. He uses high quality animations to focus on the intuitions behind what is going on in the math at hand. He also has a number of videos breaking down interesting problems and exposing their inner beauty. Also be sure to check out his website 3blue1brown.com.
  • Numberphile and Mathologer: These two channels are fairly similar (but not the same). They focus on presenting a variety of different math topics, trivia, problems, and history in bite-sized, digestible chunks. They are high quality and entertaining.
  • PBS Infinite Series: This was a PBS web show focused on exploring and explaining mathematics. It is similar to PBS Space Time (mentioned below). Sadly, the show was discontinued, but the 65 episodes are still available and worth a watch.
  • BlackPenRedPen: This channel features many videos which explain various important techniques, but I mostly know it for his epic single take integration marathons.
  • Professor Leonard: Professor Leonard posts full length lectures on a variety of topics such as calculus, linear algebra, and differential equations. His is a clear presenter and does a solid job of building understanding in his audience. 
  • MajorPrep: While this channel is technically aimed at helping engineering students prepare for their majors and their careers, the man behind has focused most of his latest videos on mathematics. His videos are high quality and he does a good job of explaining the topic at hand and showing how it can be used to solve real world problems.
  • Andrew Dotson: Again, technically not a math channel, but Andrew presents a number of in-depth derivation videos for topics in physics. He is also skilled at making comedy videos.
  • PBS Space Time: While this series focuses on space, physics, and astrophysics, it makes frequent use of mathematical reasoning in order to make sense of the universe. Seeing math used in context like this helps to build an appreciation for the origins and uses of advanced mathematics.

Websites

  • Khan Academy: Often one of the first responses that appears when someone asks where they should start learning is Khan Academy. Clearly, the site has an excellent reputation. There are lessons and resources for everything math related starting with  counting and going all the way through calculus, differential equations, and linear algebra. Best of all, it’s free. While I have not personally used the site much, what I’ve seen of it has been well crafted.
  • Paul’s Online Math Notes: This website has notes, practice problems, and solutions available for algebra, calculus 1- 3, and differential equations. The notes are accessible on the site or they can be downloaded for free. 
  • Patrick’s Just Math Tutorials: A large collection of free video tutorials and example problems from algebra, calculus, discrete math, and a few other subjects.
  • American Mathematical Society
  • Mathematical Association of America
  • European Mathematical Society
  • ProofWiki: This is an absolute life saver sometimes. The wiki contains thousands of proofs and definitions. It is helpful to search and can be fun to simply browse.
  • Coursera: This is a platform to take online courses in mathematics and other topics. 
  • Brilliant.org: I have not used this service myself, but I see a number of people speak highly of it. They offer a number of courses related to mathematics and computer science. It is worth a look.
  • Open Education Resources Commons: This site has a listing of almost three hundred free courses and textbooks from a variety of other sources. 
  • Open Textbook Library: An online collection of free math textbooks for a large array of different math subjects. 

Communities

Despite what some media depictions would have you believe, mathematics is not a solo activity. It is best learned, enjoyed, and done with others. Here are some of my favorite math-related communities from around the internet. 

  • The Math Stack Exchange: This site allows users to submit questions and to answer other’s questions. There are many knowledgeable and helpful members here, and tens of thousands of previously answered questions which may help you.
  • Quora: Despite not always having the greatest reputation in other quarters, Quora is a solid platform for questions and answers relating to mathematics. 

Reddit

Reddit has a vibrant mathematics community, spread over several different subreddits. The content focus and intended audience is a bit different in each subreddit, so knowing what to expect in each one is helpful.

  • r/learnmath: This is my favorite of the math subreddits. This community of around 150 thousand members is focused on helping people learn math. The subreddit is a sort of middle ground between r/math and r/askmath. The content is largely questions focused on understanding rather than computation. People often write exceptional responses to posts that are always worth the read. Highly recommended.
  • r/math: This is the main mathematics subreddit. The primary content is math news, discussions, and high level questions. Most of the math discussed here is upper undergraduate and graduate level mathematics. While the audience is quite broad (almost a million members), there seems to be a higher concentration of PhDs, professors, and professional mathematicians here than in some of the other subreddits.
  • r/askmath: This is a much smaller community with under twenty thousand members. The content here is mostly just people asking for computational help with specific homework problems. It’s a bit hit or miss sometimes, but it is still a decent place to find help or to improve your skills by helping others. The math here is largely algebra and calculus related.
  • r/mathmemes: As I said above, math is best enjoyed with others and what better way to enjoy something then by sharing some inside jokes with people who get it? Whether it is bad teachers, wonky proofs, unintuitive concepts, or math fails, this subreddit pokes fun at them all. It is also a great place to find quality memes to spice up and math group chats you may have with classmates. You math be surprised how much math you can actually pick up from people joking about it.
  • r/mathjokes: Just like mathmemes, except in text form.