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频道帖子
| 2 |  ✅ Follow @math | 540 |
| 3 |  ♾ The Ultimate Self-Taught Math Roadmap
Most people who want to learn math run into the same problem.
There are thousands of recommendations, hundreds of textbooks, and endless debates about what to study. What’s usually missing is the order.
This roadmap organizes some of the best mathematics books into a progression that takes you from basic proofs to advanced topics like analysis, algebra, topology, probability, and number theory.
➕ How to Prove It — Daniel Velleman
The best place to start. Teaches mathematical logic, proof writing, and how mathematicians actually think.
➕ Book of Proof — Richard Hammack
A free alternative that covers the same foundations in a more concise format.
➕ An Introduction to Mathematical Reasoning — Peter Eccles
A beginner-friendly introduction to proofs with extra emphasis on numbers and counting.
➕ Concepts of Modern Mathematics — Ian Stewart
A tour of the major ideas in modern mathematics without requiring advanced knowledge.
➕ What Is Mathematics? — Courant & Robbins
A classic overview of the field that has inspired generations of mathematicians.
➕ Calculus — Michael Spivak
The gold standard for learning calculus through rigorous reasoning rather than memorization.
➕ Calculus, Volume 1 — Tom Apostol
A more structured and comprehensive alternative for readers who prefer systematic learning.
➕ Visual Complex Analysis — Tristan Needham
One of the most beautiful math books ever written. Uses visual intuition to explain complex analysis.
➕ Principles of Mathematical Analysis — Walter Rudin
A famous and challenging analysis textbook that develops true mathematical maturity.
➕ Linear Algebra Done Right — Sheldon Axler
A proof-based approach to linear algebra focused on understanding concepts deeply.
➕ Introduction to Linear Algebra — Gilbert Strang
The most widely used applied linear algebra textbook, especially popular in engineering and data science.
➕ A Book of Abstract Algebra — Charles Pinter
A friendly introduction to groups, rings, and fields.
➕ Topology — James Munkres
The standard textbook for learning modern topology.
➕ Elementary Number Theory — Gareth & Mary Jones
A strong introduction to the mathematics of integers, primes, and divisibility.
➕ The Cauchy-Schwarz Master Class — J. Michael Steele
A collection of elegant problems that teach mathematical creativity.
➕ Introduction to Probability, Statistics, and Random Processes — Hossein Pishro-Nik
A complete introduction to probability and statistics that is freely available online.
➕ The Art of Problem Solving — Lehoczky & Rusczyk
Excellent training for mathematical problem-solving and creative thinking.
➕ Prime Numbers and the Riemann Hypothesis — Mazur & Stein
An accessible look at one of the most famous unsolved problems in mathematics.
➕ Coding the Matrix — Philip Klein
A practical approach to linear algebra through programming and real-world applications.
The biggest lesson from the roadmap is simple:
Don't try to read everything.
Pick the book that matches your current level, work through the exercises, and keep moving. Mathematics is less about talent and more about spending enough time with the right problems.
✅ Follow @math | 756 |
| 4 |  “Every living being is an engine geared to the wheelwork of the universe. Though seemingly affected only by its immediate surrounding, the sphere of external influence extends to infinite distance.”
— Nikola Tesla
✅ Follow @math | 913 |
| 5 |  The Broken Bridge of Math! (Limit vs Value)
✅ Follow @math | 1 007 |
| 6 |  ✅ Follow @math | 1 002 |
| 7 |  🤣🤣🤣
✅ Follow @math | 1 094 |
| 8 |  This ever happened to you?
✅ Follow @math | 1 022 |
| 9 |  The beauty of math and physics and teachers who work hard to expand our minds
✅ Follow @math | 1 099 |
| 10 |  This is why your teacher told you to learn math if you want to succeed in life
✅ Follow @math | 1 191 |
| 11 |  The visual demonstration of (a+b)³.
✅ Follow @math | 1 343 |
| 12 |  The shortest-known paper in a math journal. Just two sentences.
✅ Follow @math | 1 573 |
| 13 |  The Spanish company Arbore is taking inspiration from M.C. Escher's tessellated lizards for their floor designs.
✅ Follow @math | 1 735 |
| 14 |  Multiplication hacks
✅ Follow @math | 1 759 |
| 15 |  🎞 8 Great Movies About Mathematics
Most math movies aren't really about mathematics.
They're about obsession, genius, discipline, and the people behind the equations.
➕A Beautiful Mind
The story of John Nash, a brilliant mathematician whose battle with schizophrenia becomes as important as his work.
➕ Good Will Hunting
A gifted young genius can solve impossible problems, but struggles to solve his own life.
➕ Hidden Figures
The true story of the women mathematicians whose calculations helped NASA reach space.
➕ The Imitation Game
Alan Turing races to crack Nazi codes during World War II, helping change the course of history.
➕ Moneyball
A baseball team uses statistics instead of intuition to compete against richer rivals.
➕ Pi
A mathematician becomes obsessed with finding a hidden pattern that explains everything.
➕ Gifted
A child prodigy faces a difficult choice between a normal childhood and an extraordinary future.
➕ Stand and Deliver
Based on a true story of a teacher who helped underprivileged students master calculus against all expectations.
The common theme in all of them isn't mathematics.
It's what happens to people when they dedicate their lives to solving difficult problems.
✅ Follow @math | 1 843 |
| 16 |  If you need to multiply 1034482758620689655172413793 by 3, all you need to do is bring the last digit to the front.
✅ Follow @math | 1 763 |
| 17 |  Which Math Side You’ll Prefer?
✅ Follow @math | 2 093 |
| 18 |  Indices Formulas
✅ Follow @math | 2 100 |
| 19 |  Australia vs. Japan
✅ Follow @math | 2 440 |
| 20 |  90%failed to solve this tricky trig question
✅ Follow @math | 2 339 |
