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About this course
Some choose the subject because it is beautiful, others because it is practical, and yet others for some combination of these reasons. Mathematics is wonderful training for the mind, a great training if you are thinking of being a lawyer for example, and it has an increasing range of applications, from the study of the genome and climate change to financial mathematics and medical statistics. Mathematics has always been the language of physics, and, with the advent of computer modeling, is an essential component of almost all science.
An undergraduate degree in mathematics opens the door to many professions and to graduate study in a wide variety of disciplines. The American Math Society's website shows the variety of careers open to people who major in mathrelated fields.
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Eligibility Criteria
To be wellprepared for a college like Barnard, it is important to think about the academic community you are hoping to join. Barnard's general education requirements cover a wide range of subjects: literature, the social sciences, language and the arts, lab sciences, and quantitative areas. For this reason, you should acquire a strong foundation in high school, taking courses from the core academic subjects: math, science, English, history, and foreign language. Do your best to take the most rigorous classes available to you in which you can do your best work. For transfer students, our recommendations are similar. Take courses that are recommended to fulfill general requirements in the humanities, social sciences, and natural sciences. If an area is a relative weakness, continue taking that subject while pursuing advanced coursework in areas of relative strength. Remember, we hope to see how you might contribute to our intellectual community, and your choices tell us what kind of a student you will be.
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Course Modules
Requirements for the Major
The major programs in both Mathematics and Applied Mathematics are appropriate for students who plan to continue their training in graduate school. The major in Mathematical Sciences combines the elements of Mathematics, Computer Science and Statistics. It is designed to prepare students for employment in business, administration, and finance, and also give excellent background for someone planning graduate study in a social science field. Students who plan to obtain a teaching qualification in mathematics should plan their course of study carefully with an advisor, since courses that are too far from mathematics do not count towards certification
For a major in Mathematics: 14 courses as follows:
Four courses in calculus or Honors Mathematics AB, including Advanced Placement Credit. Six courses in mathematics numbered at or above 2000, and four courses in any combination of mathematics and cognate courses. The courses in mathematics must include:
MATH UN2010  Linear Algebra (also satisfied by Honors Math AB)  
MATH GU4041  Introduction to Modern Algebra I (I)  
MATH GU4042  Introduction to Modern Algebra II (II)  
MATH GU4061  Introduction To Modern Analysis I (I)  
MATH GU4062  Introduction To Modern Analysis II (II)  
MATH UN3951  Undergraduate Seminars in Mathematics I (at least one term)  
or MATH UN3952  Undergraduate Seminars in Mathematics II 
* 
Note: It is strongly recommended that the sequences MATH GU4041 Introduction to Modern Algebra I  MATH GU4062 Introduction To Modern Analysis II and MATH GU4061 Introduction To Modern Analysis I  MATH GU4062 Introduction To Modern Analysis II be taken in separate years. 
However, students who are not contemplating graduate study in mathematics may replace one or both of the two terms of MATH GU4061 Introduction To Modern Analysis I  MATH GU4062 Introduction To Modern Analysis II by one or two of the following courses: MATH UN2500 Analysis and Optimization, MATH UN3007 Complex Variables, or MATH GU4032 Fourier Analysis and may replace MATH GU4042 Introduction to Modern Algebra II by one of MATH UN3020 Number Theory and Cryptography or MATH UN3025 Making, Breaking Codes. In exceptional cases, the chair will approve the substitution of certain more advanced courses for those mentioned above.
For a major in Applied Mathematics: 14 courses
Four courses in calculus or Honors Mathematics AB, including Advanced Placement Credit.
MATH UN2010  Linear Algebra (also satisfied by Honors Math AB)  
MATH GU4061  Introduction To Modern Analysis I  
APMA E4901  Seminar: Problem in Applied Mathematics  
APMA E4903  Seminar: Problems in Applied Mathematics  
APMA E3900  Undergraduate Research in Applied Mathematics (APMA E3900 may be replaced, with approval, by another technical elective for seniors that involves an undergraduate thesis or creative research report) 
Additional electives, to be approved by the Applied Math Committee, e.g.:
MATH UN2500  Analysis and Optimization  
MATH UN3007  Complex Variables  
or MATH GU4065  Honors Complex Variables  
or APMA E4204  Functions of a Complex Variable  
MATH UN3027  Ordinary Differential Equations  
or MATH UN2030  Ordinary Differential Equations  
MATH UN3028  Partial Differential Equations  
or APMA E4200  Partial Differential Equations  
MATH GU4032  Fourier Analysis  
APMA E4300  Computational Math: Introduction to Numerical Methods  
APMA E4101  Introduction to Dynamical Systems  
APMA E4150  Applied Functional Analysis 
6 from Mathematics, 5 from a combination of Statistics and Computer Science and 3 electives from a combination of Mathematics, Statistics, Computer Science.
Mathematics  
Six required courses:  
MATH UN1101  Calculus I  
MATH UN1102  Calculus II  
MATH UN1201  Calculus III  
MATH UN2010  Linear Algebra (also satisfied by Honors Math AB)  
MATH UN2000  An Introduction to Higher Mathematics  
MATH UN2030  Ordinary Differential Equations  
or MATH UN3027  Ordinary Differential Equations  
Possible further courses selected from the following:  
MATH UN1202  Calculus IV  
MATH UN2500  Analysis and Optimization  
MATH UN3020  Number Theory and Cryptography  
MATH UN3025  Making, Breaking Codes  
Any 3 credit MATH course numbered 2000 or above


Statistics  
Select at least one of the following:  
STAT UN1211  
SIEO GU4150  
STAT UN3105  Applied Statistical Methods  
STAT UN3107  Undergraduate Research  
Possible further courses selected from the following:  
STAT UN2024  
STAT UN2025  
STAT UN2026  
Other courses from the Statistics major list


Computer Science  
Select at least one of the following programming courses:  
Introduction to Computer Science and Programming in Java (preferred)  
Introduction to Computer Science and Programming in MATLAB  
Honors Introduction to Computer Science  
Possible further courses selected from the following:  
Other classes from the Computer Science Core


COMS W3203  Discrete Mathematics: Introduction to Combinatorics and Graph Theory  
COMS W3210  Scientific Computation  
COMS W3251  Computational Linear Algebra 
More generally, electives may be any course with a prerequisite of at least one semester of Calculus, Statistics or Computer Science with the prior approval of the Mathematics Chair.
The Capstone Experience can be fulfilled by a significant thesis written under the supervision of faculty of any one of the three departments or by the Undergraduate Seminar in Mathematics.
Mathematics  
MATH UN1101  Calculus I  
MATH UN1102  Calculus II  
MATH UN1201  Calculus III  
MATH UN2010  Linear Algebra  
MATH UN2500  Analysis and Optimization  
Statistics  
STAT UN1001  Introduction to Statistical Reasoning  
or STAT UN1101  Introduction to Statistics  
or STAT UN1211  
STAT UN3105  Applied Statistical Methods  
or STAT GU4105  
STAT UN3107  Undergraduate Research  
or STAT GU4107  
STAT UN3315  
or STAT W4315  Linear Regression Models  
STAT GU4606  
or STAT GR5262  Stochastic Processes for Finance  
Computer Science  
Select one course that requires substantial work in programming  
Electives  
Select three electives from an approved selection of advanced courses in mathematics, statistics, applied mathematics, computer sciences or mathematical methods courses in physical or social sciences, including biology, economics, and physics 
Students should plan to include a senior thesis or the Undergraduate Seminar in Mathematics in their program, in consultation with their advisors.
Note: Students must obtain approval from an adviser in each of the two departments before selecting electives. Students should take MATH UN2010 Linear Algebra Linear Algebra in the second semester of the second year.
Mathematics  
Four courses in calculus or Honors Mathematics AB, including Advanced Placement Credit; and the 3 following courses:  
MATH UN2010  Linear Algebra (also satisfied by Honors Math AB)  
MATH GU4041  Introduction to Modern Algebra I  
MATH UN3951  Undergraduate Seminars in Mathematics I (at least one term)  
or MATH UN3952  Undergraduate Seminars in Mathematics II  
Computer Science  
COMS W1007  Honors Introduction to Computer Science ^{A}  
COMS W3137  Honors Data Structures and Algorithms  
COMS W3157  Advanced Programming  
COMS W3203  Discrete Mathematics: Introduction to Combinatorics and Graph Theory  
COMS W3261  Computer Science Theory  
CSEE W3827  Fundamentals of Computer Systems 
Note A: AP Computer Science with a grade of 4 or 5 or similar experience (e.g., COMS W1004) is a prerequisite for COMS W1007
Electives: 2 of the following:  
CSOR W4231  Analysis of Algorithms I  
COMS W4241  Numerical Algorithms and Complexity  
MATH UN3020  Number Theory and Cryptography  
MATH BC2006  Combinatorics  
MATH GU4061  Introduction To Modern Analysis I  
MATH UN2500  Analysis and Optimization  
MATH UN3007  Complex Variables  
MATH UN3386  Differential Geometry  
MATH GU4051  Topology 
Students seeking to pursue a Ph.D. program in either discipline are urged to take additional courses, in consultation with their advisers.
For a major in Economics and Mathematics, see the catalogue.
Requirement for the Minor in Mathematics
For a minor in Mathematics or Applied Mathematics: Six courses from any of the courses offered by the department except MATH UN1003 College Algebra and Analytic Geometry, MATH UN1101 Calculus I / MATH UN1102 Calculus II. Some cognate courses are also acceptable with prior approval from the department chair.
Requirements for the Minor in Mathematical Sciences
The minor in Mathematical Sciences comprises 6 courses, at least two from Mathematics and one from each of Statistics and Computer Science. There should be a minimum of three courses in Statistics and Computer Science. Eligible courses are any listed in the Mathematical Sciences Major with the exception of Calculus I and II.
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