📐 Mathematics Study Guide (Study In This Order)
Books within each level can often be used as alternatives to each other. You don't need to complete every book—pick the one that suits your learning style.
Level 1: Foundations
- AGS Pre-Algebra
- Fearon's Pre-Algebra
- Geometry by Jurgensen
Level 2: Algebra & Trigonometry
- College Algebra by Kaufmann
- College Algebra by Blitzer
- A Graphical Approach to Algebra and Trigonometry by Hornsby, Lial, and Rockswold
Level 3: Proofs & Discrete Math
- Discrete Mathematics with Applications by Epp
- Discrete Mathematical Structures by Kolman, Busby, and Ross
- Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand, Polimeni, and Zhang
- An Introduction to Abstract Mathematics by Bond and Keane
Level 4: Calculus
- Calculus Made Easy by Thompson
- Calculus by James Stewart
- Calculus by Michael Spivak
Level 5: Linear Algebra (Introductory)
- Elementary Linear Algebra by Howard Anton
- Schaum's Linear Algebra
- Linear Algebra by Strang
Level 6: Differential Equations & Probability/Statistics
- A First Course in Differential Equations by Zill
- Ordinary Differential Equations with Applications by Andrews
- A First Course in Probability by Ross
- Mathematical Statistics by Wackerly, Mendenhall, and Scheaffer
Level 7: Analysis
- Analysis 1 and Analysis 2 by Terrance Tao
- Advanced Calculus by Fitzpatrick
- Elements of Analysis by Ross
- Principles of Mathematical Analysis by Rudin
Level 8: Abstract Algebra
- Abstract Algebra by Saracino
- Contemporary Abstract Algebra by Gallian
- Algebra by Artin
Level 9: Linear Algebra (Advanced)
- Linear Algebra by Friedberg, Insel, and Spence
- Linear Algebra by Hoffman and Kunze
- Linear Algebra by Lang
Level 10: Topology, Complex Analysis & Combinatorics
- Introduction to Topology by Gamelin and Greene
- Naive Set Theory by Halmos
- Fundamentals of Complex Analysis by Saff and Snider
- Complex Variables and Applications by Brown and Churchill
- Applied Combinatorics by Tucker
- Graph Theory by Gould
Level 11: Graduate-Level
- Real Analysis by Royden
- Real and Complex Analysis by Rudin
- Functional Analysis by Kreyszig