非常推荐 “Student Mathematical Library” STML 这套丛书。
国内有很多学生，其实水平仍然停留在中学数学的范畴内，习惯了初等的微积分和线性代数那些「操练」，其实完全未见识过「高等数学」的面目。
以下是截至现时为止的书目：
* A First Journey through Logic
* An Introduction to Symmetric Functions and Their Combinatorics
* Discrete Morse Theory
* Hilbert’s Tenth Problem: An Introduction to Logic, Number Theory, and Computability
* An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics
* Extremal Problems for Finite Sets
* Invitation to Ergodic Theory
* Volterra Adventures
* A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z
* From Groups to Geometry and Back
* Modern Cryptography and Elliptic Curves: A Beginner’s Guide
* Problems in Abstract Algebra
* Game Theory: A Playful Introduction
* Matrix Groups for Undergraduates: 2nd Edition
* A User-Friendly Introduction to Lebesgue Measure and Integration
* Differential Geometry: Curves — Surfaces — Manifolds, 3rd Edition
* Mathematics++: Selected Topics Beyond the Basic Courses
* Quandles: An Introduction to the Algebra of Knots
* Winding Around: The Winding Number in Topology, Geometry, and Analysis
* A First Course in the Calculus of Variations
* Asymptopia
* Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction
* Primality Testing for Beginners
* Ramsey Theory on the Integers: 2nd Edition
* Algebraic Geometry: A Problem Solving Approach
* Difference Sets: Connecting Algebra, Combinatorics, and Geometry
* The Joy of Factoring
* Computability Theory
* Geometries
* Harmonic Analysis: From Fourier to Wavelets
* Numbers and Functions: From a classical-experimental mathematician’s point of view
* Elliptic Curves, Modular Forms, and Their L-functions
* Introduction to Representation Theory
* Mostly Surfaces
* Probability Tales
* The Erdős Distance Problem
* The Game of Cops and Robbers on Graphs
* Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs
* Random Walk and the Heat Equation
* Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra
* A (Terse) Introduction to Lebesgue Integration
* A Primer on the Calculus of Variations and Optimal Control Theory
* Differential Equations, Mechanics, and Computation
* Lectures on Fractal Geometry and Dynamical Systems
* Lectures on Quantum Mechanics for Mathematics Students
* Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots
* A (Terse) Introduction to Linear Algebra
* Elementary Geometry
* Higher Arithmetic: An Algorithmic Introduction to Number Theory
* Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them
* p-adic Analysis Compared with Real
* A View from the Top: Analysis, Combinatorics and Number Theory
* Filtering and Prediction: A Primer
* Finite Fields and Applications
* Frames for Undergraduates
* Invariant Theory
* A First Course in Topology: Continuity and Dimension
* Enumerative Geometry and String Theory
* Galois Theory for Beginners: A Historical Perspective
* Lectures in Geometric Combinatorics
* Number Theory in the Spirit of Ramanujan
* Geometry and Billiards
* Heads or Tails: An Introduction to Limit Theorems in Probability
* Mathematical Modelling: A case studies approach
* Matrix Groups for Undergraduates
* Six Themes on Variation
* Transformation Groups for Beginners
* An Introduction to Lie Groups and the Geometry of Homogeneous Spaces
* Computable Functions
* Elementary Algebraic Geometry
* Lectures on Generating Functions
* Problems in Mathematical Analysis III: Integration
* Basic Set Theory
* Cryptography: An Introduction
* An Introduction to Game-Theoretic Modelling: 2nd Edition
* Introduction to Topology
* Plane Algebraic Curves
* Plateau’s Problem: An Invitation to Varifold Geometry, Revised Edition
* Problems in Mathematical Analysis II: Continuity and Differentiation
* An Introduction to the Mathematical Theory of Waves
* Codes and Curves
* Exploring the Number Jungle: A Journey into Diophantine Analysis
* Inversion Theory and Conformal Mapping
* Problems in Mathematical Analysis I: Real Numbers, Sequences and Series
* The Game’s Afoot! Game Theory in Myth and Paradox
* The Mathematics of Soap Films: Explorations with Maple®
* The Prime Numbers and Their Distribution
* Lectures on Contemporary Probability
* Miles of Tiles
网站在此：
（注：目前这套丛书有95本，英语版每本平均US$44元左右，全套大概￥2万7千！
这反映了很多想学习科技／数学的人买不起原版书籍的问题。
就算美国人，我印象中他们也觉得这些书很贵。）
