“3Blue1brown”. 2021. 3Blue1brown.com. https://www.3blue1brown.com/.
3Blue1Brown is primarily a YouTube channel, but here you can find written and interactive adaptations of the lessons.
“Collection Of The Best Mathematics And Science Stuff | Abakcus”. 2022. Abakcus. https://abakcus.com/.
The internet is like an ocean. Mostly, it is so beautiful and wonderful. Once, Newton said, “What we know is a drop, what we don’t know is an ocean.” Why don’t you make your drop utterly valuable? We believe that learning new things is crucial for happiness. Abakcus is the collection of perfect sources about mathematics and science. On Abakcus, you can actively search and discover all the best articles, books, projects, videos, and tools you’re looking for.
Amit, Alon. 2023. Quora. https://www.quora.com/profile/Alon-Amit.
My undergrad degree included Mathematics, Computer Science and Physics. It was roughly a “triple degree” though I emphasized math more. I earned an MSc in math with a thesis in Category Theory and a PhD with a thesis combining Graph Theory with some aspects of Probability Theory, Algebra and Topology. I really love Number Theory. I do not know everything there is to know in math.
“Brilliant | Learn Interactively”. 2022. brilliant.org. https://brilliant.org/home/.
Our principles
Brilliant creates a culture of learning around inquiry, curiosity, and openness to failure. All of our courses are written with these principles of learning in mind.
Effective math and science learning…
- Excites.
The greatest challenges to education are disinterest and apathy. - Cultivates curiosity.
Questions and storytelling that cultivate natural curiosity are better than the threat of a test. - Is active.
Effective learning is active, not passive. Watching a video is not enough. - Is applicable.
Use it or lose it: it is essential to apply what you’re learning as you learn it. - Is community driven.
A community that challenges and inspires you is invaluable. - Doesn’t discriminate.
Your age, country, and gender don’t determine what you are capable of learning. - Allows for failure.
The best learners allow themselves to make many mistakes along their journey. - Sparks questions.
The culmination of a great education isn’t knowing all the answers — it’s knowing what to ask.
“BrainMatters.” 2018. brainmatterslearning.com. December 18, 2018. https://brainmatterslearning.com/.
At BrainMatters Learning, we believe school is more than just grades and tests—it’s the foundation for your future. Think about it: you spend 17+ years of your life in school from kindergarten to college. That’s a big chunk of time! Why not make the most of it by learning skills and habits that will help you succeed, not just in school, but in life?
“Crystal X.” 2024. Medium. Accessed December 25. https://medium.com/@tracyrenee61.
I have over fifty years of experience in the world of work, working in fast food, the military, business, non-profits, and the healthcare sector.
Excellent source for statistics!!
⭐ “GeeksForGeeks | A Computer Science Portal For Geeks”. 2023. GeeksForGeeks. https://www.geeksforgeeks.org/.
Not just for computer science!
Machine Learning is the field of study that gives computers the capability to learn without being explicitly programmed. Math is the core concept in machine learning which is used to express the idea within the machine learning model. Topics include Linear Algebra and Matrix, Regression, Geometry, Dimensionality Reduction, Vector Calculus, Vector Models, and Probability Distribution.
The Engineering Mathematics Tutorials includes Discrete Mathematics : Propositional and First Order Logic, Set Theory, Combinatorics, Probability, Graph Theory, and Engineering Mathematics : Linear Algebra, Calculus, Statistics and Numerical Methods.
The Learn Data Structures and Algorithms | DSA Tutorial includes Learn Data Structures : Array, String, Linked List, Matrix/Grid, Stack, Queue, Heap, Hash, Tree Data Structures, Binary Tree, Binary Search Tree, Other Tree Data Structures, Graph Data Structure, and Learn Algorithms : Searching Algorithm, Sorting Algorithm, Divide and Conquer Algorithm, Greedy Algorithms, Recursion, Backtracking Algorithm, Dynamic Programming, Pattern Searching, Mathematical Algorithms, Geometric Algorithms, Bitwise Algorithms, Randomized Algorithms, Branch and Bound Algorithm
“Khan Academy | Free Online Courses, Lessons & Practice”. 2021. Khan Academy. https://www.khanacademy.org/.
Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computing, history, art history, economics, and more, including K-14 and test preparation (SAT, Praxis, LSAT) content. We focus on skill mastery to help learners establish strong foundations, so there’s no limit to what they can learn next!
⭐ “LibreTexts Mathematics Library”. 2013. Mathematics LibreTexts. https://math.libretexts.org/.
Welcome to the Mathematics Library. This Living Library is a principal hub of the LibreTexts project, which is a multi-institutional collaborative venture to develop the next generation of open-access texts to improve postsecondary education at all levels of higher learning. The LibreTexts approach is highly collaborative where an Open Access textbook environment is under constant revision by students, faculty, and outside experts to supplant conventional paper-based books.
Lloyd, Philip. 2023. Quora. https://www.quora.com/profile/Philip-Lloyd-2.
I have been HOD [Head of Mathematics] mathematics in several prestigious New Zealand schools and have mentored many teachers and student teachers. I continue to do this in my retirement. I have 10 websites containing my original resources FREE for anybody to use. I also have over 70 videos on YouTube.
“Mathigon – Textbook Of The Future”. 2021. Mathigon. https://mathigon.org/.
Unleash your creativity with the world’s best manipulatives! Engage in problem-solving, explore patterns and collaborate with others.
Mad Hatter, The. 2021. “Martin Gardner Home Site”. martin-gardner.org. http://martin-gardner.org/.
Who was Martin Gardner?
First and last, he was a skeptic, who was most well known as a Scientific American, writer and annotator. This mere mortal was a mathematician, magician & mysterian, who turned out to be a big inspiration to several generations of people all over the world.
To some, Martin was the best friend mathematics ever had, and to others he was one of the most influential magicians of the last century. He’s universally acknowledged as the founding father of the modern skeptical movement, and his written legacy includes over 100 books, from his best selling Annotated Alice to dozens of classics on recreational mathematics and puzzles.
“Math Is Fun”. 2021. mathsisfun.com. https://www.mathsisfun.com/.
Math can be fun with the right tools and techniques. Math is Fun is a free web tool that explains math concepts in easy-to-understand language using puzzles, games, worksheets, and an illustrated dictionary suited for K-12 kids, teachers, and parents.
⭐ “Resources for Math Majors.” 2025. Marktomforde.com. 2025. https://marktomforde.com/academic/mathmajors/mathmajors.html.
As you proceed in your mathematical education, you will find upper level math courses to be quite a bit different from lower level math courses. (In fact, many math majors do not get a really good understanding of what mathematics is until their junior or senior year of undergraduate studies.) Upper level math courses have greater emphasis on conceptual understanding, abstraction, and the ability to modify known results to deal with new situations.
TRANSITIONING TO ADVANCED COURSES. There are different expectations in upper level courses: You will be expected to read your textbook and do more of the work on your own; you will be expected to write proofs and communicate mathematical ideas and arguments; more time will be spent on conceptual understanding and less time will be spent on computation.
You will start to see these differences a bit in sophomore-level courses (such as a Linear Algebra class or an Introduction to Proofs class), and the differences will be even more pronounced in higher-level courses, where typically much greater emphasis is placed on understanding theorems and writing proofs.
Textbook Recommendations for Self Study
Stapel, Elizabeth. 2023. “Struggling With Algebra Concepts Or Methods? Help Is Here!”. Purplemath. https://www.purplemath.com/index.htm.
Purplemath’s algebra lessons are informal in their tone, and are written with the struggling student in mind. Don’t worry about overly-professorial or confusing language! The free lessons on this math website emphasize the practicalities rather than the technicalities, demonstrating dependably helpful techniques, warning of likely “trick” test questions, and pointing out common student mistakes.
“Wolfram Mathworld: The Web’s Most Extensive Mathematics Resource”. 2021. mathworld.wolfram.com. https://mathworld.wolfram.com/.
⭐ “xaktly.com”. 2023. xaktly.com. https://xaktly.com/index.html.
This site is a collection of the math and science notes I have used in my high school math and science classes. It has become a sort of constantly-evolving electronic textbook, but I hope one that is a bit more direct, helpful and friendlier than many textbooks.
⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.
The featured image on this page is from the Small Business TRENDS website.
Mathematical Mysteries 