MIT OpenCourseWare

數學(Mathematics)

Professor Victor Guillemin works with a student in February 2000
2002年2月,Victor Guillemin教授和一名學生一起研究問題。
Professor Victor Guillemin works with a student in February 2000.

數學系的大學部課程對於學生未來就讀數學研究所和資訊科學研究所都是很好的基礎,對於直接就業的學生來說,在數學相關的領域工作:系統分析、作業研究、精算也將會擁有紮實的基礎。

因為數學系大學部學生的生涯目標五花八門,因此每個人的學習計畫都是透過學生和他們的顧問老師來特別量身定做的。一般來說,我們鼓勵學生探究數學的不同領域,包括了純粹數學和應用數學。

對於數學有深入興趣的大學生我們會鼓勵他參與高階的數學研討活動。這通常是在大一或是大二的第一個學期進行。能夠參與這些由研究數學的學者所主持的研討會,對於這些準備攻讀研究所的學生來說會是很寶貴的經驗。

大學部有三種數學學士的課程規劃:一般性數學學位、針對想要鑽研應用數學的應數學位、針對想要研究純數的理論數學學位。第四種學士學位規劃則是針對有興趣研究理論資訊科學的數學與資訊科學學位。

若要瞭解更多資訊,請前往http://www-math.mit.edu/

其他微積分資源

  • 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.

目前上線課程


大學部
課號課程名稱
18.01
2003秋季課程:單變數微積分
(Single Variable Calculus, Fall 2003)
18.013A
2001秋季課程:微積分及應用
(Calculus with Applications, Fall 2001)
18.013A
2005春季課程:微積分及應用
(Calculus with Applications, Spring 2005)
NEW!
18.014
2002秋季課程:微積分及理論I
(Calculus with Theory I, Fall 2002)
18.024
2003春季課程:微積分及理論II
(Calculus with Theory II, Spring 2003)
18.03
2004春季課程:微分方程
(Differential Equations, Spring 2004)
18.034
2004春季課程:微分方程式榮譽課程
(Honors Differential Equations, Spring 2004)
18.04
1999秋季課程:複變與應用
(Complex Variables with Applications, Fall 1999)
18.04
2003秋季課程:複變與應用
(Complex Variables with Applications, Fall 2003)
18.05
2005春季課程:機率與統計學導論
(Introduction to Probability and Statistics, Spring 2005)
NEW!
18.06
2002秋季課程:線性代數
(Linear Algebra, Fall 2002)
18.06
2005春季課程:線性代數
(Linear Algebra, Spring 2005)
NEW!
18.062J
2002秋季課程:資訊科學數學(SMA 5512)
(Mathematics for Computer Science (SMA 5512), Fall 2002)
18.062J
2005春季課程:資訊科學數學
(Mathematics for Computer Science, Spring 2005)
NEW!
18.062J
2005秋季課程:資訊科學數學
(Mathematics for Computer Science, Fall 2005)
NEW!
18.06CI
2004春季課程:線性代數:溝通強化課程
(Linear Algebra - Communications Intensive, Spring 2004)
18.085
2002秋季課程:工程師數學方法I
(Mathematical Methods for Engineers I, Fall 2002)
18.091
2005春季課程:數學闡述
(Mathematical Exposition, Spring 2005)
NEW!
18.097
2005春季課程:數學闡述
(Mathematical Exposition, Spring 2005)
NEW!
18.100B
2002秋季課程:分析I
(Analysis I, Fall 2002)
18.101
2004秋季課程:分析II
(Analysis II, Fall 2004)
18.101
2005秋季課程:分析II
(Analysis II, Fall 2005)
NEW!
18.103
2004春季課程:傅立葉分析:理論與應用
(Fourier Analysis - Theory and Applications, Spring 2004)
18.112
2005秋季課程:複合變數之函式
(Functions of a Complex Variable, Fall 2005)
NEW!
18.152
2004秋季課程:偏微分導論
(Introduction to Partial Differential Equations, Fall 2004)
18.238
2002秋季課程:幾何與量子場理論
(Geometry and Quantum Field Theory, Fall 2002)
18.303
2004秋季課程:線性偏微分方程式
(Linear Partial Differential Equations, Fall 2004)
18.310
2004秋季課程:應用數學原理
(Principles of Applied Mathematics, Fall 2004)
18.310
2002秋季課程:應用數學原理
(Principles of Applied Mathematics, Fall 2002)
18.311
2003春季課程:應用數學原理
(Principles of Applied Mathematics, Spring 2003)
18.312
2005春季課程:代數組合
(Algebraic Combinatorics, Spring 2005)
NEW!
18.314
2005秋季課程:組合分析
(Combinatorial Analysis, Fall 2005)
NEW!
18.330
2004春季課程:數值分析導論
(Introduction to Numerical Analysis, Spring 2004)
18.353J
2005秋季課程:非線性力學I:渾沌
(Nonlinear Dynamics I: Chaos, Fall 2005)
NEW!
18.361J
2002春季課程:製作模型及模擬導論
(Introduction to Modeling and Simulation, Spring 2002)
18.400J
2002春季課程:自動機、可計算性與複雜性
(Automata, Computability, and Complexity, Spring 2002)
18.400J
2005春季課程:自動機、可計算性與複雜性
(Automata, Computability, and Complexity, Spring 2005)
NEW!
18.410J
2001秋季課程:演算法導論
(Introduction to Algorithms, Fall 2001)
18.410J
2005秋季課程:演算法導論(SMA 5503)
(Introduction to Algorithms (SMA 5503), Fall 2005)
NEW!
18.413
2004春季課程:錯誤更正碼(ECC)實作
(Error-Correcting Codes Laboratory, Spring 2004)
18.433
2003秋季課程:組合最佳化
(Combinatorial Optimization, Fall 2003)
18.440
2005秋季課程:機率與隨機變數
(Probability and Random Variables, Fall 2005)
NEW!
18.441
2002春季課程:統計推論
(Statistical Inference, Spring 2002)
18.443
2003秋季課程:應用統計
(Statistics for Applications, Fall 2003)
18.700
2005秋季課程:線性代數
(Linear Algebra, Fall 2005)
NEW!
18.701
2003秋季課程:代數I
(Algebra I, Fall 2003)
18.702
2003春季課程:代數II
(Algebra II, Spring 2003)
18.704
2004秋季課程:代數與數理論研討會:橢圓曲線上的有理點
(Seminar in Algebra and Number Theory: Rational Points on Elliptic Curves, Fall 2004)
18.781
2003春季課程:數論
(Theory of Numbers, Spring 2003)
18.901
2004秋季課程:拓樸概論
(Introduction to Topology, Fall 2004)
18.904
2005秋季課程:拓撲數學研討會
(Seminar in Topology, Fall 2005)
NEW!
18.950
2005春季課程:微分幾何學
(Differential Geometry, Spring 2005)
NEW!
18.994
2004秋季課程:幾何研討會
(Seminar in Geometry, Fall 2004)
18.996VP
2002秋季課程:廣義相對論與重力輻射
(General Relativity and Gravitational Radiation, Fall 2002)
18.S34
2002秋季課程:問題解決方法研討
(Problem Solving Seminar, Fall 2002)
18.S34
2004秋季課程:問題解決方法研討
(Problem Solving Seminar, Fall 2004)
NEW!
18.S66
2003春季課程:計數的技巧
(The Art of Counting, Spring 2003)

研究所
課號課程名稱
18.075
2004秋季課程:工程師的高等微積分
(Advanced Calculus for Engineers, Fall 2004)
18.085
2005秋季課程:工程師數學方法I
(Mathematical Methods for Engineers I, Fall 2005)
NEW!
18.086
2005春季課程:工程師數學方法II
(Mathematical Methods for Engineers II, Spring 2005)
NEW!
18.117
2005春季課程:一些複合變數議題
(Topics in Several Complex Variables, Spring 2005)
NEW!
18.125
2003秋季課程:測度與積分
(Measure and Integration, Fall 2003)
18.155
2004秋季課程:微分分析
(Differential Analysis, Fall 2004)
NEW!
18.155
2002秋季課程:微分分析
(Differential analysis, Fall 2002)
18.156
2004春季課程:微分分析
(Differential Analysis, Spring 2004)
18.175
2005春季課程:機率理論
(Theory of Probability, Spring 2005)
NEW!
18.305
2004秋季課程:科學與工程的高等分析法
(Advanced Analytic Methods in Science and Engineering, Fall 2004)
18.306
2004春季課程:進階偏微分方程式及應用
(Advanced Partial Differential Equations with Applications, Spring 2004)
18.315
2005春季課程:組合理論:圖表理論、極值與數值組合之導論
(Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics, Spring 2005)
NEW!
18.315
2004秋季課程:組合學:超平面的安排
(Combinatorial Theory: Hyperplane Arrangements, Fall 2004)
18.319
2005秋季課程:幾何組合
(Geometric Combinatorics, Fall 2005)
NEW!
18.325
2005秋季課程:應用數學之議題:奈米光電中之數學方法
(Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005)
NEW!
18.327
2003春季課程:凌波、濾波器與應用
(Wavelets, Filter Banks and Applications, Spring 2003)
18.335J
2004秋季課程:數值方法導論
(Introduction to Numerical Methods, Fall 2004)
18.335J
2001秋季課程:應用數學數值方法I
(Numerical Methods of Applied Mathematics I, Fall 2001)
18.336
2004春季課程:應用數學數值方法II
(Numerical Methods of Applied Mathematics II, Spring 2004)
18.336
2005春季課程:應用數學數值方法II
(Numerical Methods of Applied Mathematics II, Spring 2005)
NEW!
18.337J
2003春季課程:應用平行運算
(Applied Parallel Computing, Spring 2003)
18.338J
2004秋季課程:無限隨機矩陣理論
(Infinite Random Matrix Theory, Fall 2004)
18.366
2005春季課程:隨機漫步與擴散運動
(Random Walks and Diffusion, Spring 2005)
NEW!
18.366
2003春季課程:隨機漫步與擴散運動
(Random Walks and Diffusion, Spring 2003)
18.376J
2004秋季課程:波傳導
(Wave Propagation, Fall 2004)
18.385
2002秋季課程:非線性力學與渾沌
(Nonlinear Dynamics and Chaos, Fall 2002)
18.385J
2004秋季課程:非線性力學與渾沌
(Nonlinear Dynamics and Chaos, Fall 2004)
NEW!
18.404J
2002秋季課程:計算理論
(Theory of Computation, Fall 2002)
18.405J
2001秋季課程:進階複雜理論
(Advanced Complexity Theory, Fall 2001)
18.409
2002春季課程:演算法行為
(Behavior of Algorithms, Spring 2002)
18.415J
1999秋季課程:高等演算法
(Advanced Algorithms, Fall 1999)
18.415J
2001秋季課程:高等演算法
(Advanced Algorithms, Fall 2001)
18.415J
2005秋季課程:高等演算法
(Advanced Algorithms, Fall 2005)
NEW!
18.416J
2002秋季課程:隨機演算法
(Randomized Algorithms, Fall 2002)
18.417
2004秋季課程:計算分子生物學導論
(Introduction to Computational Molecular Biology, Fall 2004)
18.426J
2003春季課程:密碼學中的進階議題
(Advanced Topics in Cryptography, Spring 2003)
18.435J
2003秋季課程:量子運算
(Quantum Computation, Fall 2003)
18.437J
2001秋季課程:分散式演算法
(Distributed Algorithms, Fall 2001)
18.437J
2005秋季課程:分散式演算法
(Distributed Algorithms, Fall 2005)
NEW!
18.465
2004春季課程:統計學議題:統計學習理論
(Topics in Statistics: Statistical Learning Theory, Spring 2004)
NEW!
18.465
2005春季課程:統計學議題:非參數性統計分析與頑強性
(Topics in Statistics: Nonparametrics and Robustness, Spring 2005)
NEW!
18.466
2003春季課程:數理統計
(Mathematical Statistics, Spring 2003)
18.725
2003秋季課程:代數幾何
(Algebraic Geometry, Fall 2003)
18.755
2004秋季課程:李群導論
(Introduction to Lie Groups, Fall 2004)
18.965
2004年秋季課程:集合幾何
(Geometry of Manifolds, Fall 2004)
18.996
2004春季課程:隨機矩陣及其應用
(Random Matrix Theory and Its Applications, Spring 2004)
18.996
2002春季課程:理論電腦科學議題:網際網路研究問題
(Topics in Theoretical Computer Science : Internet Research Problems, Spring 2002)
18.996A
2004春季課程:簡單理論
(Simplicity Theory, Spring 2004)
18.997
2004春季課程:組合最佳化專題
(Topics in Combinatorial Optimization, Spring 2004)

大學部/研究所
課號課程名稱