# 수학 독학 커리큘럼 정리

제가 공부하려고 개인적으로 정리한 리스트입니다.

따라서, 각 커리큘럼에 대한 문의나 질문은 이 곳에 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

## 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