Students may complete a major or minor in Mathematics. With the major, students may complete the requirements for secondary school certification. Majors may complete an M.A. in Mathematics, if accepted into the combined A.B./M.A. program, or may enter the 3-2 Program in Engineering and Applied Science at the California Institute of Technology.

**Faculty**

Leslie C. Cheng, Associate Professor and Chair

Victor J. Donnay, Professor (on leave semester I)

Helen G. Grundman, Professor

Rhonda J. Hughes, Professor (on leave semester II)

Peter G. Kasius, Instructor

Paul Melvin, Professor

Amy N. Myers, Mathematics Program Coordinator and Lecturer

Lisa Traynor, Professor

Rebecca Marie Vandiver, Postdoctoral Fellow in Mathematics and Biology

The Mathematics curriculum is designed to expose students to a wide spectrum of ideas in modern mathematics, train students in the art of logical reasoning and clear expression, and provide students with an appreciation of the beauty of the subject and of its vast applicability.

**Major Requirements**

A minimum of 10 semester courses is required for the major, including the six core courses listed below and four electives at or above the 200 level.

**Core Requirements:**

MATH B201 Multivariable Calculus (H121 or H216)

MATH B203 Linear Algebra (H215)

MATH B301 Real Analysis I (H317)

MATH B303 Abstract Algebra I (H333)

MATH B302 Real Analysis II (H318) or MATH B304 Abstract Algebra II (H334)

MATH B398 or B399 Senior Conference

With the exception of Senior Conference, equivalent courses at Haverford or elsewhere may be substituted for Bryn Mawr courses with approval of the major adviser. In consultation with a major adviser, a student may also petition the department to accept courses in fields
outside of mathematics as electives if these courses have serious mathematical content appropriate to the student’s program.

Mathematics majors are encouraged to complete their core requirements other than Senior Conference by the end of their junior year. Senior Conference must be taken during the senior year. Students considering the possibility of graduate study in mathematics or related fields are urged to go well beyond the minimum requirements of the major. In such cases, a suitable program of study should be designed with the advice of a major adviser.** **

**Honors**

A degree with honors in mathematics will be awarded by the department to students who complete the major in mathematics and also meet the following further requirements: at least two additional semesters of work at the 300 level or above (this includes Supervised Work 403), completion of a meritorious project consisting of a written thesis and an oral presentation of the thesis, and a major grade point average of at least 3.6, calculated at the end of the senior year.

**Minor Requirements**

The minor requires five courses in mathematics at the 200 level or higher, of which at least two must be at the 300 level or higher.

**Advanced Placement**

Students entering with a 4 or 5 on the Calculus AB advanced placement test will be given credit for MATH 101 and should enroll in MATH 102 as their first mathematics course. Students entering with a 4 or 5 on the Calculus BC advanced placement test will be given credit for MATH 101 and 102, and should enroll in MATH 201 as their first mathematics course. All other students are strongly encouraged to take the Mathematics Placement Exam so they can be best advised.

**A.B./M.A. Program**

For students entering with advanced placement credits it is possible to earn both the A.B. and M.A. degrees in an integrated program in four or five years.

**3-2 Program in Engineering
and Applied Science**

See the description of the 3-2 Program in Engineering and Applied Science, offered in cooperation with the California Institute of Technology, for earning both an A.B. at Bryn Mawr and a B.S. at Cal Tech.

**MATH B001 Fundamentals of Mathematics **

Basic techniques of algebra, analytic geometry, graphing, and trigonometry for students who need to improve these skills before entering other courses that use them, both inside and outside mathematics. Placement in this course is by advice of the department and permission of the instructor.

(Staff)

**MATH B005 Math Workshop **

Review of arithmetic and introduction to the basics of elementary and intermediate algebra for students whose mathematical backgrounds require such support. This course prepares students to take either MATH 001 or MATH 104 immediately thereafter. Placement in this course is by advice of the department.

(Swann)

This is a half-credit course.

**MATH B101, B102 Calculus with Analytic Geometry I and II **

Differentiation and integration of algebraic and elementary transcendental functions, with the necessary elements of analytic geometry and trigonometry; the fundamental theorem, its role in theory and applications, methods of integration, applications of the definite integral, infinite series. May include a computer lab component. Prerequisite: math readiness or permission of the instructor. Students in the calculus sequence need a grade of 2.0 or better to continue with the next course.

(Hughes, Kasius, Myers, Division II and Quantitative Skills)

MATH B104 Elements of Probability and Statistics

This course introduces students to key concepts in both descriptive and inferential statistics. Students learn how to collect, describe, display, and interpret both raw and summarized data in meaningful ways. Topics include summary statistics, graphical displays, correlation, regression, probability, the law of averages, expected value, standard error, the central limit theorem, hypothesis testing, sampling procedures, and bias. Students learn to use statistical software to summarize, present, and interpret data. This course may not be taken after any other statistics course. Prerequisite: math readiness or permission of instructor.

(Grundman, Quantitative Skills)

**MATH B201 Multivariable Calculus **

Vectors and geometry in two and three dimensions, partial derivatives, extremal problems, double and triple integrals, line and surface integrals, Green’s and Stokes’ Theorems. May include a computer lab component. Prerequisite: MATH 102 or permission of instructor.

(Hughes, Swann, Division II and Quantitative Skills)

**MATH B203 Linear Algebra **

Matrices and systems of linear equations, vector spaces and linear transformations, determinants, eigenvalues and eigenvectors, inner product spaces and quadratic forms. May include a computer lab component. Prerequisite: MATH 102 or permission of instructor.

(Staff, Division II and Quantitative Skills)

**MATH B205 Theory of Probability with Applications**

Random variables, probability distributions on Rn, limit theorems, random processes. Prerequisite: MATH 201.

(Staff, Division II and Quantitative Skills)

*Not offered in 2010-11.*

**MATH B206 Transition to Higher Mathematics**

An introduction to higher mathematics with a focus on proof writing. Topics include active reading of mathematics, constructing appropriate examples, problem solving, logical reasoning, and communication of mathematics through proofs. Students will develop skills while exploring key concepts from algebra, analysis, topology, and other advanced fields. Corequisite: MATH 203; not open to students who have had a 300-level math course.

(Kasius, Division II: Natural Science)

**MATH B210 Differential Equations with Applications **

Ordinary differential equations, including general first-order equations, linear equations of higher order and systems of equations, via numerical, geometrical, and analytic methods. Applications to physics, biology, and economics. Corequisite: MATH 201 or 203.

(Donnay, Division II and Quantitative Skills)

**MATH B221 Introduction to Topology and Geometry**

An introduction to the ideas of topology and geometry through the study of knots and surfaces in three-dimensional space. The course content may vary from year to year, but will generally include some historical perspectives and some discussion of connections with the natural and life sciences. Corequisite: MATH 201 or 203.

(Swann, Division II and Quantitative Skills)

**MATH B225 Introduction to Financial Mathematics **

Topics to be covered include market conventions and instruments, Black-Scholes option-pricing model, and practical aspects of trading and hedging. All necessary definitions from probability theory (random variables, normal and lognormal distribution, etc.) will be explained. Prerequisite: MATH 102. ECON 105 is recommended.

(Staff, Division II: Natural Science)

*Not offered in 2010-11.*

**MATH B231 Discrete Mathematics **

An introduction to discrete mathematics with strong applications to computer science. Topics include set theory, functions and relations, propositional logic, proof techniques, recursion, counting techniques, difference equations, graphs, and trees.

(Cheng, Division II and Quantitative Skills)

Cross-listed as CMSC B231

**MATH B261 Introduction to Harmonic Analysis and Wavelets **

A first introduction to harmonic analysis and wavelets. Topics to be covered: Fourier series, Fourier transform, wavelets, and their applications, including signal processing and medical imaging. Prerequisite: MATH 203 or permission of instructor.

(Cheng, Division II: Natural Science)

*Not offered in 2010-11.*

**MATH B290 Elementary Number Theor**y

Properties of the integers, divisibility, primality and factorization, congruences, Chinese remainder theorem, multiplicative functions, quadratic residues and quadratic reciprocity, continued fractions, and applications to computer science and cryptography. Prerequisite: MATH 102.

(Staff, Division II: Natural Science)

*Not offered in 2010-11.*

**MATH B295 Select Topics in Mathematics**

This course covers topics that are not part of the standard departmental offerings and varies from semester to semester. Students may take this course more than once. In spring 2011 the topic will be probability and mathematical statistics. This course will introduce the mathematical theory of probability, including density functions and distribution functions, joint and marginal distributions, conditional probability, and expected value and variance. It then will develop the theory of statistics, including parameter estimation and hypothesis testing. The emphasis is on proving results in mathematical statistics rather than on applying statistical methods. Prerequisite: MATH 201 or permission of instructor.

(Ross, Division II: Natural Science)** **

**MATH B301, B302 Introduction to Real Analysis I and II**

The real number system, elements of set theory and topology, continuous functions, uniform convergence, the Riemann integral, power series, Fourier series and other limit processes. Prerequisite: MATH 201.

(Traynor, Division II: Natural Science)

**MATH B303, B304 Abstract Algebra I and II**

Groups, rings, and fields and their homomorphisms. Quotient groups, quotient rings, and the isomorphism theorems. Standard examples including symmetric groups, free groups, and finitely generated abelian groups; integral domains, PID’s and UFD’s, and polynomial rings; finite and infinite fields. Sylow theory and field extensions. Additional topics may include: Galois theory, modules and canonical forms of matrices, algebraic closures, and localization. Prerequisite: MATH 203.

(Grundman, Kasius, Division II: Natural Science)** **

**MATH B304 Abstract Algebra II **

Groups, rings, and fields and their homomorphisms. Quotient groups, quotient rings, and the isomorphism theorems. Standard examples including symmetric groups, free groups, and finitely generated abelian groups; integral domains, PID’s and UFD’s, and polynomial rings; finite and infinite fields. Sylow theory and field extensions. Additional topics may include: Galois theory, modules and canonical forms of matrices, algebraic closures, and localization. Prerequisite: MATH 203.

(Grundman, Division II: Natural Science)

**MATH B308 Applied Mathematics I **

In spring 2011, this course will teach students to build models using finite dynamical systems, Boolean networks, linear algebra, abstract algebra, and probabilistic methods. Applications to gene regulation, biochemical reaction networks, DNA sequencing, and phyogenetics will be studied. Prerequisite: MATH 303 or permission of instructor.

(Vandiver, Division II: Natural Science)

**MATH B311 Partial Differential Equations **

Heat and wave equations on bounded and unbounded domains, Laplace’s equation, Fourier series and the Fourier transform, qualitative behavior of solutions, computational methods. Applications to the physical and life sciences. Prerequisite: MATH 301 or permission of instructor.

(Staff, Division II: Natural Science)

*Not offered in 2010-11.*

**MATH B312 Topology **

General topology (topological spaces, continuity, compactness, connectedness, quotient spaces), the fundamental group and covering spaces, introduction to geometric topology (classification of surfaces, manifolds). Typically offered yearly in alternation with Haverford. Corequisite: MATH 301, MATH 303, or permission of instructor.

(Melvin, Division II: Natural Science)

**MATH B322 Functions of Complex Variables **

Analytic functions, Cauchy’s theorem, Laurent series, calculus of residues, conformal mappings, Moebius transformations. Prerequisite: MATH 301 or permission of instructor.

(Staff, Division II: Natural Science)

*Not offered in 2010-11.*

**MATH B390 Number Theory **

Algebraic number fields and rings of integers, quadratic and cyclotomic fields, norm and trace, ideal theory, factorization and prime decomposition, lattices and the geometry of algebraic integers, class numbers and ideal class groups, computational methods, Dirichlet’s unit theorem. Prerequisite: MATH 303 or permission of instructor.

(Grundman, Division II: Natural Science)

*Not offered in 2010-11.*** **

**MATH B395 Research Seminar **

A research seminar for students involved in individual or small group research under the supervision of the instructor. With permission, the course may be repeated for credit. Prerequisite: Permission of instructor.

(Staff)

**MATH B396 Research Seminar **

A research seminar for students involved in individual or small group research under the supervision of the instructor. With permission, the course may be repeated for credit. Prerequisite: Permission of instructor.

(Staff)

**MATH B398 Senior Conference **

A seminar for seniors majoring in mathematics. Topics vary from year to year.

(Melvin)

**MATH B399 Senior Conference **

A seminar for seniors majoring in mathematics. Topics vary from year to year.

(Staff)

**MATH B403 Supervised Work **

(Staff)

**MATH B501, B502 Graduate Analysis I and II **

(Cheng)

**MATH B503, B504 Graduate Algebra I and II **

(Grundman).

*Not offered in 2010-11.*

**MATH B505, B506 Graduate Topology I and II**

(Melvin, Traynor)

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