수학 독학 커리큘럼
제가 공부하려고 개인적으로 정리한 리스트입니다.
따라서, 각 커리큘럼에 대한 문의나 질문은 여기에 해주시면 감사하겠습니다.
Start
with Algebra
Pre-Algebra는 ‘자연수, 정수, 분수, 소수, 백분율, 실수, 1차 방정식, 기초 기하학, 그래프’로 구성돼 ‘일반적인 경우’ 중등 교육으로 학습했을 것이므로 생략 가능 단계로 생각합니다.
- Pre-Algebra, Nichols
- Elementary Algebra, Sullivan, Struve, Mazzarella
or with Discrete Math
Pick one of below, but 2-4 are really hard. I would take 1 & 2.
- Discrete Mathematical Structures, Kolman, Busby, Ross
- Concrete Mathematics, Graham, Knuth, Patashnik
- or Discrete Mathematics and its Applications, Rosen
- or Discrete and Combinatorial Mathematics, Grimaldi
or Jump right into Proof Writing
Recommended book was ‘How to Prove it’.
- How To Prove It, Velleman
- or Foundations of Higher Mathematics, Fletcher, Patty
- or An Introduction To Abstract Mathematics, Bond, Keane
- or How to Read and Do Proofs, Solow
Pre-Calculus & Trigonometry
- Precalculus, Stewart, Redlin, Watson
- or Algebra and Trigonometry, Stewart, Redlin, Watson
Calculus
- Calculus, Stewart
- or Thomas’ Calculus
- or Calculus, Larson, Edwards
- or Calculus, Swokowski
Differential Equations
- Differential Equations, Zill
- Differential Equations, Nagle, Saff, Snider
- or Schaum’s Differential Equations
Probability & Statistics
- Elementary Statistics, Weiss
- or Mathematical Statistics and Data Analysis, Rice
Geometry
- Geometry, Jurgensen
Linear Algebra
- Elementary Linear Algebra, Anton
- Linear Algebra, Friedberg, Insel, Spence
Complex Variables
- Schaum’s Complex Variables
- Fundamentals of Complex Analysis, Saff, Snider
- or Complex Variables, Brown, Churchill
- or Complex Variables, Ablowitz, Fokas (Advanced)
Partial Differential Equations
- Introduction to Partial Differential Equations, Zachmanoglou, Thoe
- Partial Differential Equations, Miller
Abstract Algebra
- Abstract Algebra, Saracino
- Algebra, Lang (Said ‘considered as bibile of abstract algebra)
Real Analysis
- Introduction to Real Analysis, Bartle, Sherbert
- Advanced Calculus, Fitzpatrick
- Advanced Calculus, Buck
Number Theory
any one of below
- Number Theory, Long
- Number Theory, Andrews
- Number Theory, Dudley
Graph Theory
- Graph Theory, Gould
Topology
- Topology, Gamelin, Greene
- or Topology, Munkres
Others
- All The Math You Missed, Thomas A. Garrity
- Cryptography, Trappe
- Advanced Engineering Mathematics, Erwin Kreyszig
- Basic Mathematics, Lang