Unit 1　Precalculus

　Text (A) Functions

　Reading Material (A)　Function, Graph, Arithmetic, Imaginary Unit

　Text (B) Composite Functions and Inverse Functions

　Text (C) Logarithms and Trigonometry

　Reading Material (B) Triangle

Unit 2　Geometry

　Text (A) Analytic Geometry of R2

　Text (B) Analytic Geometry of R3

　Reading Material (A) Geometry

　Reading Material (B) Conic section

　Reading Material (C) Interview with Shiing Shen Chern

Unit 3　Algebra

　Text (A) Polynomial Equations

　Text (B) Linear Systems, Matrix Algebra, Gaussian Elimination

Reading Material (A) Gauss Prize·New Prize in Science Promotes Mathematics as a Key Technology

　Reading Material (B) Andre Weil： A Prologue

Unit 4　Set Theory

　Text (A) Set Theory (Ⅰ)

　Reading Material (A) Set Theory (Ⅱ)

Unit 5　Mathematical Analysis ( Ⅰ )

　Text (A) The Real Number System

　Text (B) Limits

　Text (C) Continuous Functions

　Text (D) Differential Calculus

　Reading Material (A)　Nonstandard Analysis

Unit 6　Mathematical Analysis ( Ⅱ )

　Text (A) Integral Calculus

　Text (B) Infinite Series

　Reading Material (A) Carleson Receives 2006 Abel Prize

Unit 7　Number Theory

　Text (A) LOO-KENG HUA (November 12,1910-June 12,1985)

　Text (B) Fundamental Ideas in Number Theory

　Reading Material (A) Prime number

Unit 8　Abstract Algebra

　Text (A) Foundations of Abstract Algebra

　Text (B) van der Waerden's Modern Algebra

　Reading Material (A) Interview with Bartel Leendert van der Waerden

　Text (C) Algebraic Geometry

Unit 9　Mathematical Analysis (Ⅱ)

　Text (A) Differential Calculus of Functions of Several Variables

　Reading Material (A) Mathematical Challenges of the 21st Century: A Panorama of Mathematics

　Text (B) Integral Calculus of Functions of Several Variables

　Reading Material (B) Hermann Weyl (November 9, 1885-December 9, 1955)

Unit 10　Differential Equations

　Text (A) Ordinary Differential Equations

　Text (B) Peter Lax Receives 2005 Abel Prize

　Reading Material (A) Interview with Louis Nirenberg

Unit 11　Higher Algebra (Ⅱ)

　Text (A) Vector Spaces

　Text (B) Linear Transformations

　Reading Material (A) Matrix

　Reading Material (B) Algebra

Unit 12　Topology

　Text (A) Basic Topology

　Reading Material (A) Topology

　Reading Material (B) Algebraic Topology

Unit 13　Numerical Analysis

　Text (A) Introduction and Basic Functional Analysis

　Text (B) Iterative Methods for Nonlinear System

　Reading Material (A) Initial Value Problems

Unit 14 Mathematical Research and Progress in Mathematics

　Text (A) But How Do I Do Mathematical Research?

　Text (B) 2006 Fields Medals Awarded

Vocabulary Index

Bibliography