MATHEMATICS AND haverford.edu/mathematics

The courses in the Department of Mathematics the requirements, but are of course prerequisites and Statistics aim to: for all subsequent courses in mathematics. • promote rigorous thinking in a systematic, deductive, intellectual discipline. Intermediate Calculus/Linear Algebra • help students identify and articulate This category includes MATH 215, 121 or 216. mathematical and statistical problems that These courses are taught for the benefit of both they encounter, both in formal academic work majors and non-majors, but are the real and elsewhere. “introduction” to math for most majors. • foster technical competence in mathematics and statistics as an aid to the better Core Major Courses comprehension of the physical, biological, and This category includes MATH 317-318 (Analysis) social sciences. and MATH 333-334 (Algebra). These courses are • guide and direct majors toward an interest in the “cornerstone” of the major, introducing many research in the mathematical and statistical important ideas in which modern mathematics is sciences. based, and also sharpening students’ skills in mathematical discourse (i.e., careful statements of definitions, theorems, proofs). LEARNING GOALS Students taking courses in the Department of Intermediate Electives Mathematics and Statistics will think rigorously • MATH 203 (Statistical Methods and Their and systematically both within the context of the Applications) discipline and in its applications—and, ideally, throughout the liberal arts curriculum. Students • MATH 204 (Differential Equations) will learn to identify and articulate mathematical • MATH 210 (Linear Optimization and Game problems that they encounter, both in Theory) mathematics and in other disciplines. Students • MATH 218 (Probability) will develop skills necessary to engage these • MATH 222 (Introduction to Scientific problems within a mathematical and/or Computing) statistical framework. Finally, students will learn • MATH/CMSC 235 (Information and Coding how to communicate their mathematical and Theory) statistical findings to a variety of audiences. • MATH 286 (Applied Multivariate Statistical Analysis). CURRICULUM Mathematics majors take a three-year core These courses are designed for both majors and sequence of courses in calculus, linear algebra, non-majors, and provide majors an excellent abstract algebra, and analysis, designed to opportunity to explore interests outside the core provide a foundation for further study in the sequence. Students can expect at least two major areas of modern mathematics. Students electives at this level to be offered most with substantial advanced placement may semesters. We coordinate with Bryn Mawr so that complete this sequence by the end of their if a topic is not offered in a given year at sophomore year. Students who have completed Haverford, it may be offered at Bryn Mawr. the core sequence may take advanced courses in algebra, analysis, topology, or other special Advanced Electives: topics. • MATH 328 () • MATH 335-336 (Topology) Mathematics courses for majors fall into six • MATH/CMSC 340 (Analysis of Algorithms) general categories: • MATH/CMSC 345 (Theory of Computation) • MATH 390 (Advanced Topics in Algebra) Preliminary Calculus • MATH 391 (Advanced Topics in Geometry This category includes MATH 105, 118, or and Topology) advanced placement. These are not listed among • MATH 392 (Advanced Topics in Analysis) Haverford College Catalog 2017-2018 275 MATHEMATICS AND STATISTICS • MATH 394 (Advanced Topics in Discrete substitute equivalent courses in mathematics at Math and Computer Science) Bryn Mawr College for any requirement, subject • MATH 395 (Advanced Topics in to advisor approval. ) • MATH 396 (Advanced Topics in Probability MINOR REQUIREMENTS and Statistics) Mathematics minors take the same core sequence • MATH 397 (Advanced Topics in Applied as do the majors, though not necessarily to the Mathematics) same depth, followed by a selection of electives tailored to the student’s interest. Statistics minors Courses at this level are very important for take a separate core sequence in probability and students planning to go to graduate school in statistics, with later flexibility in pursuing either a mathematics or related fields. The department more applied or a more theoretical track. typically offers five to six courses at this level per year. Mathematics Minor Requirements • MATH 215 (Linear Algebra) and either MATH Other Courses: 121 (Multivariable calculus) or MATH 216 • MATH 399 (Senior Seminar): a required (Advanced Calculus). year-long group seminar for seniors that • MATH 317 (Analysis I) and MATH 333 offers advice, support, and practice in (Algebra I). preparing the senior paper and oral • Two additional electives in mathematics at the presentation. 200 level or higher. • MATH 400 (Senior Research): a required year-long course for seniors that involves Minors may substitute equivalent courses in independent work with their senior thesis mathematics at Bryn Mawr College for any advisor. requirement, subject to advisor approval. • MATH 460 (Teaching Assistantship in Mathematics): a half-credit course, in which Statistics Minor Requirements students work closely with a single faculty • One of the following courses (Introduction to member in a single course at the 100 or 200 Statistics): STAT 203, ECON 204, PSYC 200, level, offering various kinds of classroom SOCL 215 support including problem sessions, review, • STAT 286 (Applied Multivariate Statistical tutoring, and laboratory assistance. Very good Analysis) experience for students considering teaching • MATH 218 (Probability) as a career. Open to junior and senior majors • MATH 215 (Linear Algebra) by invitation, and may be taken at most twice. • MATH 121 or MATH 216 (Multivariable Does not count toward the major. Calculus) • One of the following: MAJOR REQUIREMENTS o STAT 328 (Mathematical Statistics) • MATH 215, and either MATH 121 or MATH o STAT 396 (Advanced Topics in Probability 216. and Statistics) • MATH 317 and 333, and one of MATH 318 or o ECON 304 (Econometrics) 334. o SOCL 320 (Advanced Quantitative • Four additional electives in mathematics or Methods for Sociologists). approved related courses at the 200 level or higher. At least one of these must be at the Options for the Statistics Minor 300 level. (Note: MATH 399, MATH 400, • A math minor can also be a statistics minor. If MATH 460, and MATH 480 do not count a student wants to be a math minor and a toward this requirement.) statistics minor, the following courses: STAT • The senior seminar, fall and spring. 203, ECON 204, MATH 218, STAT 286, STAT • A senior paper and oral presentation. 328 and STAT 396, cannot be counted to satisfy both the math minor and statistics We strongly advise students planning graduate minor. study in mathematics or related fields to take • A math major can also be a statistics minor. If additional courses at the 300 level. Majors may a student wants to be a math major and a 276 Haverford College Catalog 2017-2018 MATHEMATICS AND STATISTICS statistics minor, the following apply: students. o STAT 203, ECON 204 and STAT 286 cannot be counted to satisfy both the math Senior Project Learning Goals major and statistics minor requirement. Our students will engage with advanced content o At most one of the following courses can and techniques in pure mathematics, applied be counted to satisfy both the math major mathematics and statistics. They will gain and statistics minor: MATH 218, STAT ownership of the process and material through 328 and STAT 396. understanding the content and the details of the • Math majors with economics concentration: problem they are investigating, constructing If a math major wants to be an econ illustrative examples, carrying out novel concentrator and a statistics minor, MATH computations or carefully analyzing a data set. 218, STAT 286, STAT 328 and STAT 396 Our students will write clear, careful and correct cannot be counted toward both the economics mathematics/statistics, from precise definition or concentration and the statistics minor. description of a model to rigorous proofs or well- • Economics majors with math concentration: supported analyses. They will develop an oral If an economics major wants to be a math presentation that highlights the central ideas of concentrator and also a statistics minor, the their thesis work at a level appropriate for an following apply: audience in the mathematical/statistical sciences. o MATH 218, STAT 286, STAT 328 and STAT 396 cannot be counted to satisfy Senior Project Assessment both the stat minor and the math The grade for the senior thesis is determined by concentration requirement. the following: o ECON 304 cannot be counted toward the • Level of engagement with advanced statistics minor. (ECON 304 is required by mathematics or statistics. the economics major.) • Level of ownership of the material and of the writing process. For further information about the statistics • Adherence to professional standards of minor, please see the PDF supplement on the written mathematics and statistics. mathematics website, or contact the minor coordinator. The grade for the senior seminar is determined by the following: SENIOR PROJECT • Completing all the assignments in accordance A senior paper is written by each major in close with the assignment description. coordination with a faculty member. The senior • Meeting deadlines for each assignment. paper is a year-long research project that includes • Whether easily discernible progress has been both written thesis and oral presentation. All made from one assignment to another. seniors take a year-long senior seminar to • Participating. support the senior paper. In the seminar, • Quality of the poster presentation. students learn how to use library resources, how • Quality of the thesis presentation. to compose and present a poster for a poster • Quality of the final thesis. session, and take turn presenting portions of their senior papers to each other to develop their skills in constructing and giving oral presentations. CONCENTRATIONS AND INTERDISCIPLINARY MINORS In the fall of the senior year, the student begins to Mathematics majors can pursue four areas of focus on a topic (sometimes an interesting concentration: theorem, other times building a mathematical model or analyzing a data set) and works through Computer Science (more theoretical) the material with the faculty advisor. The student It may come as a surprise to some that many of completes a detailed thesis proposal, a poster the fundamental questions in computer science presentation and a “mini-paper.” In the spring, (including the famous P versus NP problem) are the student develops a core fragment of the in essence mathematical questions. Conversely, thesis, the first draft, the second draft, and the some of the deepest foundational questions about final draft of the thesis, and concludes by the nature of mathematics (such as: what presenting the thesis to faculty and fellow constitutes a proof?) are inherently Haverford College Catalog 2017-2018 277 MATHEMATICS AND STATISTICS computational in nature. Computers have also classroom and extra-classroom settings. Focused become a powerful tool in mathematical research on teaching and learning as social, political, and and its applications, both theoretical and cultural activities, the Education Program experimental. A full understanding of their challenges students to explore the relationships capability and potential can only be realized by among schooling, human development, and formal coursework in computer science. The society as they gain knowledge and skills of concentration is open to math or physics majors. educational theory and practice. Students who complete one of the Education Program options Scientific Computing (more applied) are prepared to become lifelong learners, Many disciplines in the natural and social educators, researchers, leaders and agents of sciences include a significant sub-discipline that change. is explicitly computational. Examples include astronomy, biology, chemistry, economics, and For the requirements for these concentrations, physics. In some fields, such as biology, the use of see those headings in this catalog or visit the computation has become so widespread that basic departmental website. literacy in computation is increasingly important and may soon become required. The AFFILIATED PROGRAMS Concentration in Scientific Computing gives Many of our graduates have pursued successful students an opportunity to develop a basic facility and interesting careers in various engineering with the tools and concepts involved in applying disciplines. Our 4+1 program with the University computation to a scientific problem, and to of Pennsylvania, 3/2 engineering program with explore the specific computational aspects of their CalTech, and the Master’s degree course exchange own major disciplines. agreements with Swarthmore and the University of Pennsylvania offer robust—and unique— Mathematical Economics (for majors opportunities. For more information on these interested in applying their skills to options, visit the Engineering website economic problems) (haverford.edu/engineering/). Mathematics and economics are complementary disciplines. Most branches of modern economics use mathematics and statistics extensively, and FACULTY some important areas of mathematical research Lynne Butler have been motivated by economic problems. Professor Economists and mathematicians have made important contributions to each other’s Charles Cunningham disciplines. Economist Kenneth Arrow, for Visiting Assistant Professor example, did path-breaking work in the field of mathematical optimization; and in 1994 Curtis Greene (on leave 2017-2018) mathematician John Nash was awarded the J. McLain King Professor of Mathematics Nobel Prize in economics for introducing a theory of equilibrium in non-cooperative games that has Heidi Goodson become central to contemporary economic Visiting Assistant Professor theory. Haverford’s Area of Concentration in Mathematical Economics enables students in David Lippel each of the disciplines not only to gain proficiency Visiting Assistant Professor and Laboratory in the other, but also to understand the ways in Instructor which they are related and complementary. Robert Manning Mathematics Education (for majors William H. and Johanna A. Harris Professor of interested in teaching mathematics) Computational Science The Bryn Mawr-Haverford Education Program invites students to study the discipline of Elizabeth Townsend Milicevic education; explore the interdisciplinary field of Assistant Professor educational studies; begin the path of teacher preparation for traditional classrooms; and Weiwen Miao participate in teaching experiences in a range of Chair and Professor 278 Haverford College Catalog 2017-2018 MATHEMATICS AND STATISTICS Joshua Sabloff graphical, and symbolic perspectives. Enrollment Professor in one lab hour is required. Not open to students placing into Math 121 or higher, except with Eric Stachura instructor permission. Prerequisite(s): MATH 105 Visiting Assistant Professor or placement. Not open to students with credit for MATH B102 (Calculus II) or equivalent, except Jeff Tecosky-Feldman (on leave Spring 2018) with instructor consent. (Offered Fall 2017) Senior Lecturer MATH H121 MULTIVARIABLE CALCULUS COURSES Eric Stachura, Elizabeth Townsend Milicevic MATH H103 INTRODUCTION TO Natural Science (NA), Quantitative (QU) PROBABILITY AND STATISTICS An introduction to functions of several variables, Weiwen Miao vector geometry, partial derivatives, optimization, Natural Science (NA), Quantitative (QU) Taylor’s Theorem, multiple integrals, line Basic concepts and methods of elementary integrals, and Green’s and Stokes’ Theorems. probability and quantitative reasoning, with Enrollment in one lab hour is required. practical applications. Topics include: sample Prerequisite(s): MATH 118 or equivalent average and standard deviation, normal curves, placement, or instructor consent. Not open to regression, expected value and standard error, students who have previously taken multivariable confidence intervals and hypothesis tests. calculus at the college level, either at Haverford or Crosslisted: Mathematics, Statistics; elsewhere, except with instructor consent. Prerequisite(s): Not open to students who have (Offered Fall 2017 and Spring 2018) (a) placed into 121 or higher, (b) taken 118 or higher, (c) taken any other introductory statistics MATH H199 FIRST-YEAR SEMINAR: class at Haverford or Bryn Mawr, (d) received a MATHEMATICS BEYOND CALCULUS score of 4 or 5 on the AP Statistics exam. (Offered Joshua Sabloff Fall 2017) Natural Science (NA), Quantitative (QU) Half-credit course designed to introduce and MATH H105 APPLIED MODELING WITH convey the flavor of mathematics beyond the CALCULUS introductory core sequence in calculus and linear Heidi Goodson algebra. A selection of topics will be covered, Natural Science (NA), Quantitative (QU) varying from year to year. Prerequisite(s): MATH An introduction to aspects of calculus useful in 215 is a pre- or co-requisite, or instructor consent. applied work in the natural and social sciences, (Offered Spring 2018) with a strong emphasis on developing mathematical modeling skills. Topics include MATH H203 STATISTICAL METHODS differential and integral calculus of functions of AND THEIR APPLICATIONS one variable, multivariable optimization, and Lynne Butler, Weiwen Miao modeling with differential equations. Natural Science (NA), Quantitative (QU) Applications to biology, economics, and physics. An introduction to statistical methods used to This course is taught at the level of a beginning analyze data in the natural and social sciences. It calculus course, and no prior calculus experience covers descriptive statistics, the binomial and is assumed. Prerequisite(s): Not open to students normal distributions, expected value and placing into MATH 118 or higher or with previous variance, confidence intervals and hypothesis calculus credit, except with instructor consent. testing, comparison of two samples, regression, (Offered Spring 2018) and analysis of variance. A required computer lab, using R, is taught alongside this course. MATH H118 CALCULUS: DYNAMICS AND Crosslisted: Mathematics, Statistics; INTEGRATION Prerequisite(s): MATH 118 or higher, placement Jeff Tecosky-Feldman into MATH 121 or higher, or permission of Natural Science (NA), Quantitative (QU) instructor. Students who have taken another A study of the evolution of systems defined by introductory statistics course at Haverford or difference and differential equations. Methods of Bryn Mawr may only enroll in STAT 203 with analysis come from calculus: the limit, the permission of instructor. (Offered Fall 2017 and derivative, and the integral from numerical, Spring 2018) Haverford College Catalog 2017-2018 279 MATHEMATICS AND STATISTICS MATH H204 DIFFERENTIAL EQUATIONS value problems, multiple integration, line and Eric Stachura surface integrals, parametrized surfaces, Green’s, Natural Science (NA), Quantitative (QU) Gauss’ and Stokes’ Theorems. Tools from linear An introduction to the theory of ordinary algebra are used to formulate general statements differential equations (ODEs) including algebraic of definitions, theorems and proofs. techniques for solving a single ODE or a linear Prerequisite(s): Not open to students who have system of ODEs, numerical techniques for previously taken multivariable calculus at the generating approximate solutions, geometric college level, either at Haverford or elsewhere, techniques for displaying solutions to understand except with instructor permission. Requires a their behavior, and some key theorems (such as strong background in single-variable calculus and existence and uniqueness of solutions). The a course in linear algebra, or instructor consent. course includes a focus on how ideas from linear (Offered Spring 2018) algebra and multivariable calculus can be used to classify fixed points of nonlinear systems of MATH H218 PROBABILITY ODEs. Prerequisite(s): MATH 215 and MATH Lynne Butler 121 (or 216), or instructor consent. (Offered Natural Science (NA), Quantitative (QU) Spring 2018) An introduction to . Topics include: sample spaces, combinatorics, MATH H210 LINEAR OPTIMIZATION conditional probability, independence, discrete AND and continuous random variables, functions of Curtis Greene random variables, expected value and variance, Natural Science (NA) the moment generating function, and some basic Covers in depth the mathematics of optimization limit theorems. Prerequisite(s): MATH 216 or 121 problems with a finite number of variables or instructor consent. (Offered Fall 2017) subject to constraints. Applications of linear programming to the theory of matrix games and MATH H222 SCIENTIFIC COMPUTING: network flows are covered, as well as an CONTINUOUS SYSTEMS introduction to nonlinear programming. Robert Manning Emphasis is on the structure of optimal solutions, Natural Science (NA), Quantitative (QU) algorithms to find them, and the underlying A survey of major algorithms in modern scientific theory that explains both. This course is designed computing, with a focus on continuous problems. for students interested in computer science, Topics include numerical differentiation and economics, or mathematics. Prerequisite(s): integration, numerical linear algebra, root- MATH 215 or equivalent, or instructor consent. finding, optimization, Monte Carlo methods, and (Typically offered every other year) discretization of differential equations. Basic ideas of error analysis are presented. A regular MATH H215 LINEAR ALGEBRA computer lab introduces students to the software Elizabeth Townsend Milicevic package Matlab, in which the algorithms are Natural Science (NA), Quantitative (QU) implemented and applied to various problems in An abstract introduction to linear algebra, the natural and social sciences. Crosslisted: focusing on proof techniques. Topics covered Mathematics, Computer Science; Prerequisite(s): include: vector spaces, linear transformations and MATH 215 or instructor consent. (Offered Fall matrices, determinants, eigenvalue problems, 2017) quadratic forms, and the spectral theorem. One extra hour of weekly discussions. Prerequisite(s): MATH H231 DISCRETE MATHEMATICS MATH 121 or equivalent placement, or 118 with Steven Lindell instructor consent (Offered Fall 2017 and Spring Natural Science (NA) 2018) An introduction to discrete mathematics with strong applications to computer science. Topics MATH H216 MULTIVARIABLE CALC include set theory, functions and relations, USING LINEAR ALGEBRA propositional logic, proof techniques, difference Lynne Butler equations, graphs, and trees. Crosslisted: Natural Science (NA), Quantitative (QU) Computer Science, Mathematics; Co-requisite(s): Calculus in n-dimensional Euclidean space: CMSC 105, 107, or 110, or instructor consent. continuous and differentiable functions, extreme (Offered Fall 2017) 280 Haverford College Catalog 2017-2018 MATHEMATICS AND STATISTICS MATH H286 APPLIED MULTIVARIATE Natural Science (NA) STATISTICAL ANALYSIS A rigorous treatment of fundamental algebraic Weiwen Miao structures. Topics include: introduction to Natural Science (NA), Quantitative (QU) groups, modular arithmetic, polynomials, rings, An introduction to multivariate statistical fields, Galois theory, vector spaces, and modules. analysis. The course includes methods for Prerequisite(s): MATH 215 and either 121 or 216, choosing, fitting, and evaluating multiple or instructor consent. (Offered Fall 2017) regression models and analysis of variance models. A required computer lab, using R, is MATH H334 ALGEBRA II taught alongside this course. Crosslisted: Heidi Goodson Mathematics, Statistics; Prerequisite(s): MATH Natural Science (NA) 215 and one of the following: ECON 204, MATH A continuation of Math 333. Topics include: 203, PSYC 200, SOCL 215; or instructor consent. group actions, Sylow’s theorems, representation (Typically offered every other year) theory of finite groups, finite abelian groups, Galois theory, advanced linear algebra, and MATH H317 ANALYSIS I modules. Prerequisite(s): MATH 333 or Joshua Sabloff instructor consent. (Offered Spring 2018) Natural Science (NA) A rigorous development of topics in calculus, MATH H335 TOPOLOGY including the axioms of the real number line, Staff cardinality, convergence of sequences, point-set Natural Science (NA) topology (open/closed sets, compactness, Generalizes topological concepts from Euclidean connectedness), continuity, differentiability, and spaces to arbitrary topological spaces, and the Riemann integral. The course also has a major introduces elements of algebraic topology. focus on the writing of clear and correct Concepts covered include continuity, mathematical proofs. Prerequisite(s): MATH 215 connectedness, and compactness. The course and either 121 or 216, or instructor consent. culminates in an exploration of the fundamental (Offered Fall 2017) group and covering spaces. Prerequisite(s): MATH 317 and 333 (333 can be a corequisite), or MATH H318 ANALYSIS II instructor consent. (Offered Fall 2017) Robert Manning Natural Science (NA) MATH H337 DIFFERENTIAL GEOMETRY A continuation of MATH 317, focusing on Joshua Sabloff measure theory, the Lebesgue integral, function Natural Science (NA) spaces, and sequences and series of functions A study of the differential geometry of curves and with applications (e.g., Fourier series, existence surfaces. Concepts covered include both the local and uniqueness of solutions to differential theory (including metrics, curvature, and equations). Prerequisite(s): MATH 317 or geodesics) and the global theory, including the instructor consent. (Offered Spring 2018) Gauss-Bonnet theorem. Prerequisite(s): MATH 317 or MATH 216 with special permission, or MATH H328 MATHEMATICAL instructor consent. (Offered Spring 2018) STATISTICS Weiwen Miao MATH H340 ANALYSIS OF ALGORITHMS Natural Science (NA) Sorelle Friedler An introduction to mathematical theory of Natural Science (NA) statistics. Topics include: Estimation, Hypothesis Qualitative and quantitative analysis of Testing, one-sample inference, two-sample algorithms and their corresponding data inference, and regression. Additional topics may structures from a precise mathematical point of include: goodness-of-fit tests and analysis of view. Performance bounds, asymptotic and variance. Crosslisted: Mathematics, Statistics; probabilistic analysis, worst case and average case Prerequisite(s): MATH 218 or instructor consent. behavior. Correctness and complexity. Particular (Offered Spring 2018) classes of algorithms such as sorting searching will be studied in detail. Crosslisted: MATH H333 ALGEBRA I Mathematics, Computer Science; Prerequisite(s): Heidi Goodson Haverford College Catalog 2017-2018 281 MATHEMATICS AND STATISTICS CMSC 106 or 107 or B206, and 231, or instructor Crosslisted: Computer Science, Mathematics; consent. (Typically offered every fall) Prerequisite(s): MATH 317 or MATH 333 or instructor consent. (Offered Spring 2018) MATH H345 THEORY OF COMPUTATION Steven Lindell MATH H396 ADVANCED TOPICS IN Natural Science (NA) PROBABILITY AND STATISTICS Introduction to the mathematical foundations of Curtis Greene computer science: finite state automata, formal Natural Science (NA), Quantitative (QU) languages and grammars, Turing machines, Various topics in statistics will be covered. computability, unsolvability, and computational Crosslisted: Mathematics, Statistics; complexity. Class will have a required discussions Prerequisite(s): MATH 218 and one of the session on Fridays from 10:00-11:30. Attendance following: MATH 203, ECON 203/204, PSYC required. Prerequisite(s): (CMSC 106 or CMSC 200, SOCL 215; or instructor consent. (Typically 107) and CMSC 231, and junior or senior offered every other year) standing, or instructor consent. (Offered Spring 2018) MATH H397 ADVANCED TOPICS IN APPLIED MATHEMATICS MATH H360 MATHEMATICAL Eric Stachura ECONOMICS Natural Science (NA) Giri Parameswaran An advanced course in some area of applied Social Science (SO), Quantitative (QU) math, with topics varying according to instructor. A study of advanced mathematical tools used in Recent versions have covered partial differential economic analysis. Topics include eigenvalues equations (2016, 2012, 2011) and dynamical and quadratic forms, differential equations, systems/chaos (2014, 2009). The course typically convex programming and dynamic programming. involves a mix of theory (often an extension of Applications to consumer theory, generalized ideas seen in real analysis) and computation. linear regression, stability of equilibrium, and Prerequisite(s): MATH 317 or instructor consent. models of growth and search. Fulfills Mathematic (Typically offered every other year) Economics (MTEC) concentration. Crosslisted: Economics, Mathematics; Prerequisite(s): MATH MATH H399 SENIOR SEMINAR 215; either MATH 121 or 216; ECON 203 or 204 Weiwen Miao or MATH 203 or SOCL 215 or PSYC 200 or Bryn Natural Science (NA) Mawr’s ECON B253 recommended, or instructor Seminar for students writing senior papers, consent. (Offered Fall 2017) dealing with the oral and written exposition of advanced material. (Offered Fall 2017) MATH H392 ADVANCED TOPICS IN ANALYSIS AND GEOMETRY: COMPLEX MATH H400 SENIOR RESEARCH ANALYSIS Staff Heidi Goodson Natural Science (NA) Natural Science (NA) Work on senior thesis with advisor. (Offered Fall An introduction to differentiation and integration 2017) of functions of a complex variable. Topics include the complex plane and elementary functions, complex differential calculus, integration and Cauchy’s integral formula. Applications to physical science and number theory may be discussed. Prerequisite(s): MATH 317 or instructor consent. (Typically offered every other year)

MATH H394 ADVANCED TOPICS IN THEORETICAL COMPUTER SCIENCE David Lippel Natural Science (NA)

282 Haverford College Catalog 2017-2018