Mathematical Economics
Advisers: Professors BROWN (Mathematics), ERICKSON (Mathematics), FENN (Economics), HOEL (Economics)
Students majoring in Mathematical Economics (ME) must successfully complete no fewer than 16 units of listed courses in Mathematics (MA) and Economics (EC), including a senior thesis. To solidify basic problem solving skills, all majors must initially take a common set of required courses in economic theory, calculus, statistics, and linear algebra. Contingent on individual course prerequisites, majors may then directly fulfill the elective requirement which undertakes a more advanced treatment of mathematical economics, or complete a sequence of courses that provide exposure to the statistical modeling of data. This major provides strong training for students pursuing private sector careers in investment banking, forecasting, applied mathematics, or finance, as well as graduate work in economics, operations research, and financial engineering.
Major Requirements
PREREQUISITES
Students desiring to major in ME are required to pass the following prerequisites prior to admission into the major. If a student has not taken all four of these courses, that student may be admitted only if currently scheduled for a later section or by consent of the department chair if mitigating circumstances exist.
To get started with this (and any of our department majors), students will need our gateway courses of Principles of Economics, either as a 2-block course (EC100) or as two separate blocks (EC101 and EC102). Students will also need Calculus 1 (MA125 or MA126), and Calculus 2 (MA 129),
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Principles of Economics OR Principles of Microeconomics AND Principles of Macroeconomics |
2 units |
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Calculus 1 |
1 unit |
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Calculus 2 |
1 unit |
International Baccalaureate (IB) Higher Level and Advanced Placement (AP) courses with registrar-approved test scores count as the equivalents of Economics 100, 101 and 102. Those scores, and answers to other IB and AP questions on course equivalents, can be found here: /offices/registrar/transfer-credit-guidelines.html.
DISTINCTION IN MATHEMATICAL ECONOMICS is awarded by action of both Departments (Math and Economics & Business) to up to the top 20% of graduating majors based on their GPA within the major with the provision that they have also received an A in Senior Thesis.
COURSE OF STUDY FOR THE MATHEMATICAL ECONOMICS MAJOR
To graduate as a Mathematical Economics major, students must pass the all-college requirements, while completing major components consisting of eleven units of required courses, three units of electives, and two units of senior thesis for a total of 16 units in the major.
A. Required Courses (total of 11 units)Math (6 Units)
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Calculus 1 or equivalent as approved by Math Department |
1 unit |
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Calculus 2 or equivalent as approved by Math Department |
1 unit |
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Calculus 3 |
1 unit |
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Introduction to Probability and Statistics |
1 unit |
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Applied Linear Algebra |
1 unit |
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Sequences and Series |
1 unit |
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6 Units |
Economics (5 Units)
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Principles of Economics OR Principles of Microeconomics AND Principles of Macroeconomics |
2 units |
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Microeconomic Theory |
1 unit |
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Macroeconomic Theory |
1 unit |
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Econometric Theory |
1 unit |
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5 Units |
B. Electives (total of 3 units)
- Economics elective
At least one 300 or 400 level Economics (EC) elective from the Economics and Business Department, or other as approved in advance by the Chair of the Department of Economics and Business.
- Mathematics elective
At least one elective from the following list, or other as approved in advance by the chair of the Department of Mathematics.
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Theoretical Linear Algebra |
1 unit |
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Statistical Methods I |
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Probability |
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Ordinary Differential Equations |
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1 Unit |
- Mathematical Economics elective
At least one elective from the following list, or other as approved in advance by the chair of the Department of Economics and Business.
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Advanced Topics in Mathematical Economics |
1 unit |
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Mathematical Economics of Addiction |
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Mathematical Economics of Game Theory |
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Mathematical Economics of Growth |
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1 Unit |
- EC 496 - Senior Thesis in Mathematical Economics (total of 2 units)
TOTAL MINIMUM REQUIRED CREDITS.........................................................................................16 units
Courses
Economics
An introduction to the principles of economics (both microeconomics and macroeconomics) with emphasis on decision-making by households and firms, the way in which individual markets work, the distribution of income, governmental impact on specific markets, the behavior of economic aggregates such as total output, total employment, the price level, the rate of economic growth; and government policies which affect them. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement. (Not offered 2024-25).
An introduction to the principles of microeconomics with emphasis on decision-making by households and firms, the way in which individual markets work, the distribution of income, and governmental impact on specific markets. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
An introduction to the principles of macroeconomics with emphasis on the behavior of economic aggregates such as total output, total employment, the price level, and the rate of economic growth; and government policies which affect them Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
Selected introductory topics in economics and business. Specific content and emphasis to be determined by the instructor. Exposes students to problems and trends in society which can be illuminated through application of basic tools and concepts drawn from economics and business fields. May be taught with Emphasis on Writing and Speaking.
Social entrepreneurship is the practice of identifying, starting, and growing successful mission-driven businesses, nonprofits, and social ventures - that is, organizations that strive to advance social change through innovative solutions. This course is an introduction to social entrepreneurship, an emerging field that lies at the intersection of entrepreneurship and social change. The course will review innovative leaders who are attempting to mitigate problems facing humanity and our planet today. Course materials and activities will introduce students to characteristics of the social impact leader, philanthropy skills and knowledge, scaling of social impact, and impact measurement for social ventures. Students will discuss philanthropy and giving and the ways you might contribute your time, energy, and skills to promote health, equity, peace – whatever it is you care most about – in your life beyond this course. The class will learn the complex web of individuals and organizations that make up the social impact sector before each student works to create their own social impact plan. (Summer only 2024-25).
Investigates the concept of sustainable development by first introducing students to necessary economic terms and concepts. It next explores traditional economic models of production and distribution. Finally it introduces the concept of sustainable development (meeting the needs of the present without compromising the ability of future generations to meet their own needs). The course includes fieldwork to explore the behavior of traditional economic models and examples of sustainable development. May involve additional expense $$$. Students can choose to take this course for credit either in Economics (EC 141) or Environmental Science (EV 141) (Fulfills one unit of the divisional requirement in the Social Sciences, but not in the Natural Sciences.) (Also listed as EV 141.) (Not offered 2024-25).
Examines current problems in water resource management on various scales — from local to international (transboundary) supply and quality issues. Aims to demonstrate on an introductory level the value of economic analysis in the context of other approaches for thinking about water resources issues. (Not offered 2024-25).
The course will examine sports economics models. Students will apply theory to various aspects of both collegiate and professional sports. Topics include (but are not limited to) wage discrimination in sports, the economics of stadiums, alumni giving and collegiate athletics, academics and collegiate athletics, sports rights and broadcasting, and sports and gambling. Field trips may be included.
This course develops: 1.) the tools necessary for the economic analysis of environmental and natural resource problems; 2.) the ability to apply those tools in the investigation of a real world environmental resource problem and; 3.) the insight to form policy recommendations on the basis of such analysis and investigation. Particular emphasis on problems of market failure, such as externalities, public goods, non-market goods, uncertainty, income distribution, inter-temporal resource allocation and policies to correct for imperfect markets. (Not offered 2024-25).
The economic aspects of public revenues, expenditures and debt; the different types of taxes; the interrelationship between the activity of the private and public economy. (Not offered 2024-25).
Selected topics, with content and emphasis developed by the instructor.
Examination of classic and modern conceptions of political economy. Emphasis on understanding theory and applying it to explain political and economic outcomes within states and among states in the international arena. Meets the Equity and Power: EPG requirement.
Selected topics, with content and emphasis developed by the instructor. 1.0 units (Not offered 2024-25).
This course surveys the causes and manifestations of income and wealth inequality. We begin by studying the measurement and definition of inequality and mobility and their changes over time. We then examine how skill, education, and health map onto income and wealth over a person's lifetime and transmit from generation to generation. While we review inequality in a global context, most discussion is grounded in the historical and current social and institutional conditions of the United States, focusing on race, gender, and class. Lastly, we look at the driving forces behind the large rise in inequality in recent decades: changes in technology, globalization, demographic shift, and migration. We will hone our skills in handling large datasets, extracting information from data, and visualizing it. Meets the Equity and Power: EPUS requirement.
An advanced theory of pricing for both the product and factor markets with an emphasis on the economic behavior of: 1.) the individual; 2.) the household; 3.) the firm; and 4.) the industry.
An advanced study of business cycles and economic growth models.
The use of statistical and mathematical techniques in the applied analysis of economic models. Macro- and micro-economic applications.
Application of economic concepts to analysis of environmental problems. Development of approaches to dealing with the special problems of non-market goods. Discussion of the role of economics in policy analysis. Particular emphasis on problems of market failure, i.e., externalities, public goods, non-market goods, uncertainty, income distribution, inter-temporal resource allocation and policies to correct for imperfect markets.
This course adds real-world complexity and analysis to the perfectly competitive model, including transaction costs, imperfect information, and barriers to entry. The course will focus on determinants of firm and market organization and behavior, and practices such as advertising, innovation, price discrimination, and strategic behavior.
Problems of employment of labor from the standpoint of employees, employers and society including the following: economic analysis of trade unions; union types, theories, policies, methods and weapons; company and union public relations, Junior standing. (Not offered 2024-25).
Historical and economic analysis of foreign trade; theories of international trade; commercial policies and economic integration; changing patterns of trade; regional and world trade organizations.
Exploration of the field of technological change: how technologies develop and evolve; and how technologies subsequently affect our economy and society. Using case studies and journal articles as a springboard for discussion, we will apply economic concepts to events ranging from the Industrial Revolution to the present. Topics may include patent law, copyright infringement, the Green Revolution, e-commerce, health and agricultural biotechnology, and energy-related innovation. Required field study during the block, Additional expense $$$ for students. Meets the Critical Learning: CP requirement. (Not offered 2024-25).
This course applies economic theory and data analysis in an investigation of important issues in higher education. Issues of prestige, admissions, financial aid, access, student and faculty quality, alumni giving and endowments, and externalities will be addressed
An examination of consequences for home and host countries of the individual/family decision to migrate. (Not offered 2024-25).
Selected topics, with content and emphasis developed by the instructor.
Examines the economic theory and institutions of banking and other forms of financial intermediation and markets that channel savings into investment as well as the economics of financial crises, monetary policy and the government’s interaction with the financial system. Limit to be 15 when taught off campus.
What explains the current pattern of inequality of incomes between and within countries? What are the historical and contemporaneous causes of the distribution of the wealth of nations? This course gives an introduction to growth and development, focusing on the use of real-world data and theoretical and empirical research as the basis of development policies. The course aims to understand how low- and middle-income countries are institutionally, historically, or structurally different from high income countries, to learn and deploy theories and models of economic development and to understand policies that have been effective in dealing with particular problems affecting developing countries. Meets the Critical Perspectives: Global Cultures requirement.
This course utilizes economic theory to enable students to both understand and analyze the role of economic policy in the national arenas of Latin America. The course begins with an introduction to the global economic environment, the historical background of Latin America and the economic emergence of the region. The course focuses on several aspects of trade policy and regional agreements, monetary policy, fiscal policy, and their impact on the international policy environment, framing the analysis of these microeconomic and macroeconomic issues in the context of Latin America. The course will also address current events, both domestic and international, which are particularly relevant for the economic viability of the region. The purpose of the course is to understand the economic context and environment of policymaking in Latin America, as well as the impact on the different actors: workers, firms, the environment, political institutions. (Not offered 2024-25).
Historical and economic analysis of international financial arrangements; theories of foreign exchange, balance of payments and adjustment mechanisms; alternative world monetary systems in theory and practice; proposals for monetary reform; regional and world financial organization.
Selected topics, with content and emphasis developed by the instructor (Not offered 2024-25).
The use of advanced statistical and mathematical techniques in the analysis of economic models Meets the Critical Perspectives: Quantitative Reasoning requirement.
Selected topics in the study of Mathematical Economics. Specific content and emphasis are developed by the instructor(s). Topics will meet the ME elective requirement for the Mathematical Economics major. (Not offered 2024-25).
This course provides the student with the mathematical tools to explore the economic models of addiction. The course begins by exploring static demand-side models of addiction before proceeding to their dynamic counterparts. The course will rely on journal articles that explore the demand for addictive substances such as alcohol, tobacco, marijuana, and cocaine. Also explored are models that treat gambling and sports spectatorship as addictive behaviors. A limited discussion of supply-side models is also included.
Game Theory offers a framework for studying strategic interactions in a wide variety of circumstances. Most economics and business courses explore the nature of choice by individuals -- be those consumers or firms or even countries. The interdependence among decision-makers is usually captured as a constraint on the activities of the individual. Game theory broadens that perspective by allowing the agent to be aware of and to interact with other agents in dynamic and complex ways. We will set up and solve strategic and sequential form games and evaluate the quality of those outcomes. We will also consider multi-player interactions under conditions of uncertainty.
Exogenous and endogenous growth models and the effect of policy variables (functions) such as education, technical progress, and taxes on economic growth. Analysis of steady state equilibrium and convergence in levels and growth rates. Cross-sectional and panel data models of economic growth. (Not offered 2024-25).
Student readings of works selected by a faculty member on a common problem not covered directly by regular courses. Intensive research, writing, discussion, and oral reporting of ideas related to the assigned readings. Independent student work and initiative. May be taught as an extended year-long course.
A project normally organized around preparation of a substantial paper or project. Proposed and carried out at student initiative, under supervision of a department faculty member, in an area in which the student has already completed basic coursework and an elective and that extends the student’s knowledge beyond regularly offered courses.
Selected topics, with content and emphasis developed by the instructor.
Students produce original research under the personal supervision of an assigned faculty member. (Not offered 2024-25).
Selected topics, with content and emphasis developed by the instructor. (Not offered 2024-25).
Cooperation between advanced students and faculty on an individual basis to jointly pursue research on a selected topic. The student will be responsible for a share of the research, discussion of the findings and significance, and preparation of a paper reflecting the procedures and findings of the investigation. May be taught as an extended year-long course.
Focuses on the economic interactions among countries as nation states to pursue their interests as well as the role of international institutions and multilateral treaties in establishing an international economic regime. Students write a substantial paper exploring some aspect of this interaction, and have considerable freedom in defining their research agenda. (Also listed as PS 470.) (Not offered 2024-25).
A travel and research opportunity on selected economics, business or political economy topics intended to provide a learning experience in an off-campus setting. Additional prerequisites determined by the instructor relevant to the selected topic. May involve additional expense $$$. Enrollment limit based on resources available for the selected topic. (Not offered 2024-25).
Students produce original research under the personal supervision of an assigned faculty member, who normally advises no more than six thesis students.
Students produce original research under the personal supervision of an assigned faculty member, who normally advises no more than six thesis students.
Students produce original research under the personal supervision of an assigned faculty member, who normally advises no more than six thesis students.
Mathematics
An introduction to mathematical thinking through specified topics drawn from number theory, geometry, graph theory, algebra or combinatorics. The course will focus on giving students the opportunity to discover mathematics on their own. No previous mathematical background is required, but students will be expected to come with curiosity and a willingness to experiment. Not recommended for math majors. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement.
An introduction to the ideas of probability, including counting techniques, random variables and distributions. Elementary parametric statistical tests with examples drawn from the social sciences and life sciences. Not recommended for mathematics majors. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement. Meets the Critical Learning: SA requirement.
The study of systems of linear equations and matrix algebra with an emphasis on applications. Topics include the use of matrices to represent linear systems, independence and bases, invertibility, and eigenvalues. The use of computer algebra systems is emphasized. Applications will be drawn from economics, statistics, computer science, biology, and other fields. Meets the Critical Learning: FRL requirement.
Skillful teaching of mathematics requires the teacher to understand the material from a variety of perspectives, and with greater depth than his or her students. This course helps to prepare future elementary teachers by exploring some of the deeper structure of elementary mathematics. Topics will include: counting and cardinality, ratio and proportional relationships, elementary number theory, operations and algebraic thinking, and the role of axioms, deduction, examples, and counterexamples. Meets the Critical Perspectives: Quantitative Reasoning requirement. (Not offered 2024-25).
Covers the same material as MA126 together with a review of selected content from algebra, trigonometry, analytic geometry, and the study of functions. This course is recommended for students who want a more thorough review of precalculus material while studying Calculus 1. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
Introduction to calculus for functions of one variable. Focus is on the definition, methods, and applications of derivatives. Integrals are briefly introduced. Students normally begin the calculus sequence with this course if they have solid precalculus preparation and have not previously studied calculus. Students who need a thorough review of precalculus should take MA125 instead; students who have previously studied calculus should consider MA129 instead. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
Development of the definite integral, techniques of integration, and applications of the definite integral. Modeling with differential equations. Taylor polynomials and non-Cartesian coordinate systems in two dimensions. Students who have successfully completed a first course in calculus that focused on derivatives should consider this as an appropriate next course. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
Introduction to data manipulation, visualization, and Monte Carlo simulation using the statistical programming language R. The course emphasizes cleaning, organizing, and transforming raw data into a more suitable format for analysis. Students will also explore existing statistical theories through the lens of computation. Students who are interested in improving statistical computing skills should consider this course. (Not offered 2024-25).
(Summer only 2024-25).
An introduction to combinatorics, graph theory, and combinatorial geometry. The topics are fundamental for the study of many areas of mathematics as well as for the study of computer science, with applications to cryptography, linear programming, coding theory, and the theory of computing. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
Opportunity to study new mathematical ways of thinking in a cultural context. Much like the division between plants and animals in biology, mathematics can be divided into continuous mathematics (e.g. calculus) and discrete mathematics, the latter of which is the subject of this course. Includes concepts that are fundamental to modern mathematics and computer science. We will also introduce mathematics with important applications to the social sciences. Mathematical topics will be illuminated by examining their treatment in a variety of non-Western cultures, both historical and traditional. (Not offered 2024-25).
Vectors in two and three dimensions, differential and Integral calculus for functions of several variables, and the calculus of vector-valued functions. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
A calculus-based introduction to probability theory and statistical inference. Topics include probability, random variables, discrete and continuous distributions, sampling distributions, confidence intervals, hypothesis testing, and linear regression. This course also provides basic introduction to statistical programming language R. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement. Meets the Critical Learning: SA requirement.
This course will focus on the fundamentals of exploratory data analysis, hypothesis testing, and experimental design in the ecological, environmental, and the earth sciences. Topics will include theory and practice of project design, data distribution and description, the central limit theorem, characterization of uncertainty, correlation, univariate hypothesis testing, and multivariate analyses (ANOVA, linear regression). Students will complete a final project using environmental data collected in the field and analyzed using statistical computer software. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. (Not offered 2024-25).
Matrix algebra and Gaussian elimination. The geometry of vectors in R2, R3 and Rn. Vector spaces and linear transformation. Introduction to orthogonal geometry and eigenvalue problems. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
This course will focus on the theoretical foundations and processes of linear algebra. Proofs and methods of proof will be stressed throughout. Topics include abstract vector spaces and their linear transformations; linear independence, span, and bases; the rank-nullity theorem; invertibility; eigenvalues and eigenvectors; matrix factorizations; inner product spaces; orthogonal projections and orthonormal bases; singular value decomposition; positive operators. Further advanced topics may be covered if time allows. Applications of linear algebra may be introduced to bolster the theoretical discussion.
An introduction to one of the major mathematical software packages such as Mathematica or Matlab. Investigation of symbolic computation, numerical algorithms, and graphics as used in these programs. Students may take the course more than once to learn additional software packages, but they may take it a maximum of two times for credit. (May be taught either in the extended format or as a half-block.) (Not offered 2024-25).
Students will meet regularly during the semester, in order to learn problem solving techniques as applied to interesting mathematical problems, often drawn from the national William Lowell Putnam competition, or the COMAP Mathematical Modeling Contest. Students may take the course more than once, but at most two times for credit (in different years). Pass/Fail grade only. .5 units
This course will provide a forum for discussing current research and classic papers in mathematical biology. Topics will be chosen that both relate to students' research experiences and broaden their knowledge of mathematical biology. The seminar will also provide a forum for discussing research with visiting scientists. It will meet twice per block for one semester. (Not offered 2024-25).
Covers statistical methods for learning from data beyond those typically learned in introductory courses. Emphasis on statistical modeling, including multiple linear regression, classification models, and other methods for supervised learning and statistical inference. Additional techniques include non-parametric methods, bootstrap estimation, and analysis of model fit via cross-validation. Includes a strong computational component and will make use of the statistical programing language R for data analysis and simulations. Meets the Critical Learning: FRL requirement. Meets the Critical Learning: SA requirement.
Special topics in mathematics not offered on a regular basis. (Not offered 2024-25).
A careful study of major topics in elementary number theory, including divisibility, factorization, prime numbers, perfect numbers, congruences, Diophantine equations and primitive roots. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement.
An introduction to selected quantitative models drawn from areas of biology such as ecology, genetics and physiology. For each model, the course includes an investigation of the mathematical methods, an evaluation of the model, and some elementary simulation techniques. Meets the Critical Perspectives: Scientific Investigation of the Natural World requirement. Meets the Critical Perspectives: Quantitative Reasoning requirement. Meets the Critical Learning: FRL requirement. (Not offered 2024-25).
A first course in the careful study of infinity in mathematics. Convergence of sequences and series will be explored thoroughly along with selected topics from power series, Fourier series, fractals, cardinality, and complex numbers. The course emphasizes the importance of precise definitions, which allow mathematicians to construct rigorous proofs involving infinity. Meets the Critical Learning: FRL requirement.
Some current topics in advanced and modern geometry. Topics drawn from linear geometry, affine, inversive and projective geometries, foundations and axiomatics, transformation groups, geometry of complex numbers. (Offered alternate years.) (Not offered 2024-25).
Vector functions, divergence and curl, Green's and Stokes' theorems, and the properties of three-dimensional curves and surfaces. Related topics from linear algebra and differential equations. (Not offered 2024-25).
Probability spaces, discrete and continuous random variables, independence, expectation, distribution functions
Ordinary Differential Equations. Introduction to methods for finding solutions to differential equations involving a single, independent variable. Topics include linear equations, exact solutions, series solutions. Laplace transforms, Sturm Separation and Comparison Theorems, systems of equations, and existence and uniqueness theorems.
An introduction to the abstract algebraic properties of groups, rings and fields.
A study of graphs as finite mathematical structures. Emphasis on algorithms, optimization and proofs. (Offered alternate years.)
Special topics in mathematics not offered on a regular basis.
An introduction to the nature of mathematical research. Investigation with a faculty member of current mathematical problems, usually chosen from the field of the faculty member's own research. (Offered in alternate years. May be offered some years as an extended format course for 1/2 unit.) (Not offered 2024-25).
An introduction to the theoretical basis for the calculus, with an emphasis on rigorous proof. Properties of the real number system; sequences and series; continuity; elementary topology of the real line, Euclidean space and metric spaces; compactness; pointwise and uniform convergence.
Selected topics in the study of Mathematical Economics. Specific content and emphasis are developed by the instructor(s). Topics will meet the ME elective requirement for the Mathematical Economics major. (Not offered 2024-25).
An introduction to the study of point-set topology. Examples of topological spaces; compactness, connectedness, and continuity; separation axioms. Additional topics chosen from algebraic or geometric topology. (Offered alternate years.)
A study of selected developments in the history of mathematics and the role of mathematics in different cultures across time. The course often draws on original sources and traces the relationships among different fields within mathematics through the in-depth study of major unifying results. When used to fulfill the capstone requirement for the mathematics department, the course must be taken in the senior year.
The calculus of functions of a complex variable. Differentiation, contour integration, power-series, residue theory and applications, conformal mapping and applications.
Introduction to analytical and numerical methods for finding solutions to differential equations involving two or more independent variables. Topics include linear partial differential equations, boundary and initial value problems, Fourier series solutions, finite element methods, the Laplace equation, the wave equation and the heat equation.
Brief introduction of probability, descriptive statistics, classical and Bayesian statistical inference, including point and interval estimation, hypothesis tests and decision theory. (Offered alternate years.)
The development and analysis of algorithms for approximating solutions to mathematical problems. Topics covered include: approximating functions, finding roots, approximating derivatives and integrals, solving differential equations, solving systems of linear equations, and finding eigenvalues. (Not offered 2024-25).
Continuation of Mathematics 321. Topics may include Galois theory, commutative algebra, computational algebra, representations of finite groups, or algebraic geometry.
Given on demand for a group of students interested in a topic not included in the regular curriculum. (Not offered 2024-25).
Continuation of Mathematics 375. A rigorous treatment of derivatives and integrals of a single variable. Other topics, chosen by the instructor, may include a rigorous approach to multivariable calculus; the implicit and inverse function theorems; analysis on manifolds; dynamical systems; measure theory and the Lebesgue integral; functional analysis.
Advanced work in mathematics on the senior capstone project. Required for all students who are completing their capstone experience through a yearlong project and working towards the required summary seminar and summary paper. This course should be taken in the senior year, during or before Block 6