MIT OpenCourseWare

数学(Mathematics)

Professor Victor Guillemin works with a student in February 2000
2002年2月,Victor Guillemin教授和一名学生一起研究问题。
Professor Victor Guillemin works with a student in February 2000.

数学系的大学部课程对于学生未来就读数学研究所和计算机科学研究所都是很好的基础,对于直接就业的学生来说,在数学相关的领域工作:系统分析、作业研究、精算也将会拥有扎实的基础。

因为数学系大学部学生的生涯目标五花八门,因此每个人的学习计划都是透过学生和他们的顾问老师来特别量身定做的。一般来说,我们鼓励学生探究数学的不同领域,包括了纯粹数学和应用数学。

对于数学有深入兴趣的大学生我们会鼓励他参与高级的数学研讨活动。这通常是在大一或是大二的第一个学期进行。能够参与这些由研究数学的学者所主持的研讨会,对于这些准备攻读研究所的学生来说会是很宝贵的经验。

大学部有三种数学学士的课程规划:一般性数学学位、针对想要钻研应用数学的应数学位、针对想要研究纯数的理论数学学位。第四种学士学位规划则是针对有兴趣研究理论计算机科学的数学与计算机科学学位。

若要了解更多资讯,请前往http://www-math.mit.edu/

其他微积分资源

  • Textbook: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408820.
    • Instructor's Manual: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408839.
    • Study Guide: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408847.
  • Online Publication: Kleitman, Daniel. Calculus for Beginners and Artists.

An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, or actuarial science.

Because the career objectives of undergraduate mathematics majors are so diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor. In general, students are encouraged to explore the various branches of mathematics, both pure and applied.

Undergraduates seriously interested in mathematics are encouraged to elect an upper-level mathematics seminar. This is normally done during the junior year or the first semester of the senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work.

There are three undergraduate programs that lead to the degree Bachelor's of Science in Mathematics: a General Mathematics Option, an Applied Mathematics Option for those who wish to specialize in that aspect of mathematics, and a Theoretical Mathematics Option for those who expect to pursue graduate work in pure mathematics. A fourth undergraduate program leads to the degree Bachelor's of Science in Mathematics with Computer Science; it is intended for students seriously interested in theoretical computer science.

For more information, go to http://www-math.mit.edu/.

Other Calculus Resources

  • Textbook: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408820.
    • Instructor's Manual: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408839.
    • Study Guide: Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408847.
  • Online Publication: Kleitman, Daniel. Calculus for Beginners and Artists.

目前上线课程


大学部
课号课程名称
18.01
2003秋季课程:单变量微积分
(Single Variable Calculus, Fall 2003)
18.013A
2001秋季课程:微积分及应用
(Calculus with Applications, Fall 2001)
18.013A
2005春季课程:微积分及应用
(Calculus with Applications, Spring 2005)
NEW!
18.014
2002秋季课程:微积分及理论I
(Calculus with Theory I, Fall 2002)
18.024
2003春季课程:微积分及理论II
(Calculus with Theory II, Spring 2003)
18.03
2004春季课程:微分方程
(Differential Equations, Spring 2004)
18.034
2004春季课程:微分方程荣誉课程
(Honors Differential Equations, Spring 2004)
18.04
1999秋季课程:复数应用
(Complex Variables with Applications, Fall 1999)
18.04
2003秋季课程:复数应用
(Complex Variables with Applications, Fall 2003)
18.05
2005春季课程:机率与统计学导论
(Introduction to Probability and Statistics, Spring 2005)
NEW!
18.06
2002秋季课程:线性代数
(Linear Algebra, Fall 2002)
18.06
2005春季课程:线性代数
(Linear Algebra, Spring 2005)
NEW!
18.062J
2002秋季课程:计算机科学数学(SMA 5512)
(Mathematics for Computer Science (SMA 5512), Fall 2002)
18.062J
2005春季课程:计算机科学数学
(Mathematics for Computer Science, Spring 2005)
NEW!
18.062J
2005秋季课程:计算机科学数学
(Mathematics for Computer Science, Fall 2005)
NEW!
18.06CI
2004春季课程:线性代数:沟通强化课程
(Linear Algebra - Communications Intensive, Spring 2004)
18.085
2002秋季课程:工程师数学方法I
(Mathematical Methods for Engineers I, Fall 2002)
18.091
2005春季课程:数学阐述
(Mathematical Exposition, Spring 2005)
NEW!
18.097
2005春季课程:数学阐述
(Mathematical Exposition, Spring 2005)
NEW!
18.100B
2002秋季课程:分析I
(Analysis I, Fall 2002)
18.101
2004秋季课程:分析II
(Analysis II, Fall 2004)
18.101
2005秋季课程:分析II
(Analysis II, Fall 2005)
NEW!
18.103
2004春季课程:傅立叶分析:理论与应用
(Fourier Analysis - Theory and Applications, Spring 2004)
18.112
2005秋季课程:复合变数之函式
(Functions of a Complex Variable, Fall 2005)
NEW!
18.152
2004秋季课程:偏微分导论
(Introduction to Partial Differential Equations, Fall 2004)
18.238
2002秋季课程:几何与量子场理论
(Geometry and Quantum Field Theory, Fall 2002)
18.303
2004秋季课程:线性偏微分方程
(Linear Partial Differential Equations, Fall 2004)
18.310
2004秋季课程:应用数学原理
(Principles of Applied Mathematics, Fall 2004)
18.310
2002秋季课程:应用数学原理
(Principles of Applied Mathematics, Fall 2002)
18.311
2003春季课程:应用数学原理
(Principles of Applied Mathematics, Spring 2003)
18.312
2005春季课程:代数组合
(Algebraic Combinatorics, Spring 2005)
NEW!
18.314
2005秋季课程:组合分析
(Combinatorial Analysis, Fall 2005)
NEW!
18.330
2004春季课程:数值分析导论
(Introduction to Numerical Analysis, Spring 2004)
18.353J
2005秋季课程:非线性力学I:浑沌
(Nonlinear Dynamics I: Chaos, Fall 2005)
NEW!
18.361J
2002春季课程:建模与仿真导论
(Introduction to Modeling and Simulation, Spring 2002)
18.400J
2002春季课程:自动机、可计算性与复杂性
(Automata, Computability, and Complexity, Spring 2002)
18.400J
2005春季课程:自动机、可计算性与复杂性
(Automata, Computability, and Complexity, Spring 2005)
NEW!
18.410J
2001秋季课程:算法导论
(Introduction to Algorithms, Fall 2001)
18.410J
2005秋季课程:算法导论(SMA 5503)
(Introduction to Algorithms (SMA 5503), Fall 2005)
NEW!
18.413
2004春季课程:纠错码(ECC)实验
(Error-Correcting Codes Laboratory, Spring 2004)
18.433
2003秋季课程:组合最优化
(Combinatorial Optimization, Fall 2003)
18.440
2005秋季课程:机率与随机变数
(Probability and Random Variables, Fall 2005)
NEW!
18.441
2002春季课程:统计推论
(Statistical Inference, Spring 2002)
18.443
2003秋季课程:应用统计
(Statistics for Applications, Fall 2003)
18.700
2005秋季课程:线性代数
(Linear Algebra, Fall 2005)
NEW!
18.701
2003秋季课程:代数I
(Algebra I, Fall 2003)
18.702
2003春季课程:代数II
(Algebra II, Spring 2003)
18.704
2004秋季课程:代数与数理论研讨会:椭圆曲线上的有理点
(Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves, Fall 2004)
18.781
2003春季课程:数论
(Theory of Numbers, Spring 2003)
18.901
2004秋季课程:拓朴概论
(Introduction to Topology, Fall 2004)
18.904
2005秋季课程:拓扑数学研讨会
(Seminar in Topology, Fall 2005)
NEW!
18.950
2005春季课程:微分几何学
(Differential Geometry, Spring 2005)
NEW!
18.994
2004秋季课程:几何研讨会
(Seminar in Geometry, Fall 2004)
18.996VP
2002秋季课程:广义相对论与重力辐射
(General Relativity and Gravitational Radiation, Fall 2002)
18.S34
2002秋季课程:问题解决方法研讨
(Problem Solving Seminar, Fall 2002)
18.S34
2004秋季课程:问题解决方法研讨
(Problem Solving Seminar, Fall 2004)
NEW!
18.S66
2003春季课程:计数的技巧
(The Art of Counting, Spring 2003)

研究所
课号课程名称
18.075
2004秋季课程:工程师的高等微积分
(Advanced Calculus for Engineers, Fall 2004)
18.085
2005秋季课程:工程师数学方法I
(Mathematical Methods for Engineers I, Fall 2005)
NEW!
18.086
2005春季课程:工程师数学方法II
(Mathematical Methods for Engineers II, Spring 2005)
NEW!
18.117
2005春季课程:一些复合变数议题
(Topics in Several Complex Variables, Spring 2005)
NEW!
18.125
2003秋季课程:测度与积分
(Measure and Integration, Fall 2003)
18.155
2004秋季课程:微分分析
(Differential Analysis, Fall 2004)
NEW!
18.155
2002秋季课程:微分分析
(Differential analysis, Fall 2002)
18.156
2004春季课程:微分分析
(Differential Analysis, Spring 2004)
18.175
2005春季课程:机率理论
(Theory of Probability, Spring 2005)
NEW!
18.305
2004秋季课程:科学与工程的高等分析法
(Advanced Analytic Methods in Science and Engineering, Fall 2004)
18.306
2004春季课程:进阶偏微分方程及应用
(Advanced Partial Differential Equations with Applications, Spring 2004)
18.315
2005春季课程:组合理论:图表理论、极值与数值组合之导论
(Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics, Spring 2005)
NEW!
18.315
2004秋季课程:组合学:超平面的安排
(Combinatorial Theory: Hyperplane Arrangements, Fall 2004)
18.319
2005秋季课程:几何组合
(Geometric Combinatorics, Fall 2005)
NEW!
18.325
2005秋季课程:应用数学之议题:纳米光电中之数学方法
(Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005)
NEW!
18.327
2003春季课程:凌波、滤波器与应用
(Wavelets, Filter Banks and Applications, Spring 2003)
18.335J
2004秋季课程:数值方法导论
(Introduction to Numerical Methods, Fall 2004)
18.335J
2001秋季课程:应用数学数值方法I
(Numerical Methods of Applied Mathematics I, Fall 2001)
18.336
2004春季课程:应用数学数值方法II
(Numerical Methods of Applied Mathematics II, Spring 2004)
18.336
2005春季课程:应用数学数值方法II
(Numerical Methods of Applied Mathematics II, Spring 2005)
NEW!
18.337J
2003春季课程:并用平行运算
(Applied Parallel Computing, Spring 2003)
18.338J
2004秋季课程:无限随机矩阵理论
(Infinite Random Matrix Theory, Fall 2004)
18.366
2005春季课程:随机漫步与扩散运动
(Random Walks and Diffusion, Spring 2005)
NEW!
18.366
2003春季课程:随机漫步与扩散运动
(Random Walks and Diffusion, Spring 2003)
18.376J
2004秋季课程:波传导
(Wave Propagation, Fall 2004)
18.385
2002秋季课程:非线性力学与浑沌
(Nonlinear Dynamics and Chaos, Fall 2002)
18.385J
2004秋季课程:非线性力学与浑沌
(Nonlinear Dynamics and Chaos, Fall 2004)
NEW!
18.404J
2002秋季课程:计算理论
(Theory of Computation, Fall 2002)
18.405J
2001秋季课程:进阶复杂理论
(Advanced Complexity Theory, Fall 2001)
18.409
2002春季课程:算法行为
(Behavior of Algorithms, Spring 2002)
18.415J
1999秋季课程:高等算法
(Advanced Algorithms, Fall 1999)
18.415J
2001秋季课程:高等算法
(Advanced Algorithms, Fall 2001)
18.415J
2005秋季课程:高等算法
(Advanced Algorithms, Fall 2005)
NEW!
18.416J
2002秋季课程:随机算法
(Randomized Algorithms, Fall 2002)
18.417
2004秋季课程:计算分子生物学导论
(Introduction to Computational Molecular Biology, Fall 2004)
18.426J
2003春季课程:密码学中的进阶议题
(Advanced Topics in Cryptography, Spring 2003)
18.435J
2003秋季课程:量子运算
(Quantum Computation, Fall 2003)
18.437J
2001秋季课程:分布式算法
(Distributed Algorithms, Fall 2001)
18.437J
2005秋季课程:分布式算法
(Distributed Algorithms, Fall 2005)
NEW!
18.465
2004春季课程:统计学议题:统计学习理论
(Topics in Statistics: Statistical Learning Theory, Spring 2004)
NEW!
18.465
2005春季课程:统计学议题:非参数性统计分析与顽强性
(Topics in Statistics: Nonparametrics and Robustness, Spring 2005)
NEW!
18.466
2003春季课程:数理统计
(Mathematical Statistics, Spring 2003)
18.725
2003秋季课程:代数几何
(Algebraic Geometry, Fall 2003)
18.755
2004秋季课程:李群导论
(Introduction to Lie Groups, Fall 2004)
18.965
2004年秋季课程:集合几何
(Geometry of Manifolds, Fall 2004)
18.996
2004春季课程:随机矩阵及其应用
(Random Matrix Theory and Its Applications, Spring 2004)
18.996
2002春季课程:理论计算机科学议题:互联网研究问题
(Topics in Theoretical Computer Science : Internet Research Problems, Spring 2002)
18.996A
2004春季课程:简单理论
(Simplicity Theory, Spring 2004)
18.997
2004春季课程:组合最优化专题
(Topics in Combinatorial Optimization, Spring 2004)

大学部/研究所
课号课程名称