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2020-2021 Course Catalog

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This catalog was created on Sunday, June 20, 2021.


Mathematics

Professors:S. Corry (chair), K. Krebsbach (on leave term(s) I), A. Parks, B. Pourciau (on leave term(s) I, II, III)
Associate professor:J. Gregg
Assistant professors:A. Chakraborty, J. Rana (on leave term(s) III), A. Sage, E. Sattler

Pattern and form surround us—from the branching angles of our blood vessels and the complexity of computer algorithms to inventory scheduling and the four-dimensional geometry of our universe. As the pure expression of pattern and form, mathematics provides the language for science. In the past 100 years, many disciplines have been virtually transformed by the infusion of mathematics, so that alongside the traditional field of mathematical physics, one now finds new disciplines such as mathematical biology, mathematical ecology, mathematical economics, mathematical linguistics and mathematical psychology.

But mathematics is so much more than its applications. As the study of formal structures, mathematics offers a supreme beauty, an abstract forest of pattern and form, at once deep, intricate, logical, and surprising, a forest holding wonders both known and unknown. The search for these wonders is no game, for mathematics bears on eternal truth: Primes—such as 2, 3, 5, 7, 11, 13, ...—cannot be written as the product of two smaller integers. How many primes are there? Infinitely many. This is a well-known wonder proved by Euclid. Twin primes—such as 3 and 5, 5 and 7, 11 and 13, 17 and 19, ...—are “consecutive” primes. How many twin primes are there? No one knows. Mathematicians have unleashed their most sophisticated tools on this problem, but the question remains unanswered. It is an unknown wonder. Will you be the first to find the answer? Whatever the answer, it is an eternal and universal truth: true for all time, in all places, to every intellect.

To reflect the diversity of modern mathematics and its applications, the department offers a mathematics major, a statistics track through the major, and in conjunction with the economics department, an interdisciplinary major in mathematics-economics. The department's computer science major is described separately under Computer Science. In addition to a minor in mathematics, the department supports an interdisciplinary minor in Statistics and Data Science.

The first two years of our program provides an introduction to the areas of calculus, analysis, discrete mathematics, and linear algebra. These courses pave the way for exploration of diverse elective offerings at the junior and senior level. We offer courses in many areas of pure and applied mathematics, elementary and advanced statistics, and computer science. Majors engage in a one-term independent study during their senior year, working on a topic of their choice under the guidance of a faculty member. This transforming experience demonstrates a student’s ability to learn mathematics independently and to clearly and cogently express this knowledge both verbally and in writing.

The department offers a number of elementary- and intermediate-level courses designed to support other majors and meet the needs of students wishing to continue their study of mathematics, statistics, or computer science.

Lawrentians majoring in mathematics or mathematics-economics prepare themselves for a wide variety of interesting careers, but wherever life takes them, they have one thing in common—the logical and precise, yet intuitive and creative, habit of mind instilled by the serious study of mathematics and statistics together with their powerful applications.

Required for the major in mathematics

Students who major in mathematics will develop the ability to learn mathematics and statistics independently, to express their knowledge clearly and cogently, and to understand, critique, and construct mathematical and statistical arguments. They will apply the principles of careful argumentation—agree on meaning before debating truth, expose all (especially hidden) assumptions, abstract from examples, seek the underlying structure, apply logic pristinely—to critique arguments in other fields.

In addition to the general mathematics track, we also have a statistics track for students wishing to focus their upper-level work in statistics. The requirements for both tracks refer to the following categories of elective courses:

A) Algebra & Combinatorics: MATH 525, 545, 555, 565

B) Analysis & Topology: MATH 510, 530, 535, 550, 560

C) Applied Mathematics: MATH 340, 350, 400, 420, 435

D) Statistics: STAT 255, 445, 450, 455

The major in mathematics (general track) requires the following:

  1. MATH 140: Calculus, MATH 155: Multivariable Calculus
  2. MATH 200: Complex Sequences & Series, MATH 230: Discrete Mathematics, Math 250: Linear Algebra.
  3. Five 6-unit courses chosen from categories A-D; at most one of these courses may come from category D, and at least 3 of the categories A-D must be represented.
  4. One six-unit computer science (CMSC) course numbered 150 or above; one of 150, 205, or 210 is recommended.
  5. Senior Experience: completion of a 6-unit independent study project in at least one term of the senior year.

The statistics track for the mathematics major requires the following:

  1. MATH 140: Calculus, MATH 155: Multivariable Calculus.
  2. MATH 200: Complex Sequences & Series, MATH 230: Discrete Mathematics, Math 250: Linear Algebra.
  3. MATH 340: Probability.
  4. One additional MATH course from categories A-C.
  5. STAT 255: Statistics for Data Science.
  6. Two of the following courses: STAT 445: Mathematical Statistics, STAT 450: Bayesian Statistics, STAT 455: Advanced Statistical Modeling.
  7. Either CMSC/STAT 205: Data Scientific Programming or CMSC/STAT 208: Machine Learning.
  8. Senior Experience: completion of a 6-unit independent study project in at least one term of the senior year.

Required for the interdisciplinary major in mathematics-economics

Students who complete the major in mathematics-economics will pursue the outcomes described for the economics and mathematics majors with an explicit focus on economics in constructing and critiquing mathematical arguments. Students pursuing the major must have an advisor in each department.

The major in mathematics-economics requires the following:

  1. MATH 140: Calculus, MATH 155: Multivariable Calculus.
  2. MATH 200: Complex Sequences & Series, MATH 230: Discrete Mathematics, Math 250: Linear Algebra.
  3. MATH 340: Probability.
  4. One of the following courses: STAT 445: Mathematical Statistics, STAT 450: Bayesian Statistics, MATH 510: Real Analysis.
  5. ECON 100: Introductory Economics.
  6. ECON 300: Microeconomics, ECON 320: Macroeconomics, ECON 380: Econometrics.
  7. One 6-unit ECON course numbered between 400 and 580.
  8. Senior Experience: a 6-unit independent study project that has been approved by both departments.

Senior Experience in mathematics or mathematics-economics

The mathematics department's Senior Experience consists of a 6-unit (typically one-term) independent study project completed in the senior year. The project must demonstrate the capacity to learn mathematics (or statistics) independently or to utilize mathematics or mathematical technique as an innovative or substantive part of a larger project.

Interdisciplinary mathematics-economics majors must demonstrate the ability to combine topics in both disciplines—bringing appropriate techniques of mathematics or statistics to bear on the study of economics, or learning mathematics or statistics suggested by economic models.

For mathematics majors, the project must be approved and supervised by a faculty member in the mathematics department. For mathematics-economics majors, the project must be approved by a faculty member of each department and supervised by a member of one of the departments. Students should consult with departmental members in the spring before their senior year, in order to plan appropriately for their Senior Experience.

Required for the minor in mathematics

  1. MATH 140: Calculus, MATH 155: Multivariable Calculus.
  2. MATH 200: Complex Sequences & Series, MATH 230: Discrete Mathematics, Math 250: Linear Algebra.
  3. Two additional 6-unit courses chosen from categories A-D.

Required for the minor in data science

  1. Two core courses:
    1. CMSC/STAT 205: Data-Scientific Programming
    2. STAT 255: Statistics for Data Science
  2. Two statistics and data science electives from the list of:
    • CMSC/STAT 208: Machine Learning
    • CMSC/STAT 405: Advanced Data Computing
    • STAT 450: Bayesian Statistics
    • STAT 455: Advanced Statistical Modeling
  3. Two additional courses in an area of focus such as economics, biology, psychology, government, computer science, statistical theory:
    • ANTH 207: Quantitative Analysis in Anthropology
    • BIOL 170: Integrative Biology: Experimental Design and Statistics
    • BIOL 360: Introduction to Bioinformatics
    • BIOL 375: Biostatistics
    • BIOL 380: Ecological Modeling
    • CHEM 210 / CHEM 211 Analytical Chemistry and Statistical Methods in Analytical Chemistry
    • CMSC 210: Introduction to Scientific Programming
    • CMSC 470: Artificial Intelligence
    • ECON 223: Quantitative Decision Making
    • ECON 380: Econometrics
    • ECON 481: Advanced Econometrics & Modeling
    • ENST 235 / GEOS 214: Climate and Climate Change
    • ETST 302: Research Methods in Ethnic Studies
    • GOVT 271: Research Methods in Political Science
    • GOVT 538: Outside the Margin of Error: Polling and Quantitative Prediction in Modern Politics
    • MATH 340: Probability
    • PSYCH 280: Research Methods I
    • PSYCH 281: Research Methods II
    • STAT 445: Mathematical Statistics
    • STAT 450: Bayesian Statistics

Additional Stipulations:

  1. No more than one of ANTH 207 and BIOL 170 may count toward the minor.
  2. The minor requires a total of six distinct courses. Thus, courses that are listed twice above (such as STAT 450) may count toward one, but not both requirements.
  3. No more than three courses, counting toward any one major or other minor, may be counted toward the minor.

Teacher certification in mathematics

Mathematics majors can seek certification to teach math at the secondary level. Students can add an endorsement in a second area by completing an appropriate minor. Students who plan to seek teacher certification should review the requirements in the Education section of the catalog and meet with the director of teacher education, preferably before the end of the sophomore year.

First-year courses

The department offers two calculus sequences: MATH 140, 155, 200 (Calculus, Multivariable Calculus, Complex Sequences & Series) and MATH 120, 130 (Applied Calculus I, II). Students intending to major in computer science or chemistry must complete Calculus I and Multivariable Calculus. Students intending to major in mathematics or physics must take all three courses: Calculus I, Multivariable Calculus, and Complex Sequences & Series. Sufficiently prepared students should enter the calculus sequence during their first year. Sufficient preparation means strong high school mathematics, including a pre-calculus or elementary functions course. Students who lack this preparation yet need the calculus sequence should consider enrolling in MATH 103: Preparation for Calculus. In every case, all students intending to enroll in MATH 140, 155, or 200 must take the ALEKS online diagnostic exam covering topics in pre-calculus, and a score of at least 75% is required for enrollment. 

The Applied Calculus I, II sequence is designed to introduce students to the applied mathematics used in the social and life sciences. This sequence demands less technical proficiency than does the regular calculus sequence. Good performance in high school mathematics through the junior year should be adequate preparation.

For students interested in statistics:

  • Students without prior study of statistics or calculus should enroll in STAT 107: Principles of Statistics;
  • Students ​with prior study of statistics (e.g. AP statistics or BIOL 170) or credit for MATH 140 (or equivalent) should enroll in STAT 255: Statistics for Data Science. Students with credit for MATH 120 should consult with a member of the math department for placement advice.

Advanced placement

Advanced placement in the calculus sequence and 6 Lawrence units may be obtained by presenting a score of 4 or 5 on the AB or BC calculus exams administered by the College Board. Students with these scores should generally enroll in MATH 155: Multivariable Calculus after passing the ALEKS online diagnostic exam. 

Six Lawrence units (for STAT 107: Principles of Statistics) may be obtained by scoring 4 or 5 on the College Board statistics exam. Students with these scores wishing to study statistics should enroll in STAT 255: Statistics for Data Science.

Tutorials

The department views tutorials as opportunities to enhance its usual course offerings, not duplicate them. In order to reserve tutorials for this purpose, no tutorials or directed studies are given for courses routinely offered, and the department does not normally permit a tutorial to be used to satisfy any requirement for the major.

Off-campus and cooperative programs

Students wishing to combine a liberal arts degree with engineering should consider the 3-2 program in engineering.

The department encourages students to apply to the many Research Experiences for Undergraduates (REU) programs funded by the National Science Foundation; in these summer programs, students receive a stipend and participate in research teams at various campuses throughout the country. Students may also be interested in the Budapest Semester in Mathematics or in one of several other off-campus study options. Department faculty members can provide details.


Courses - Mathematics

MATH 103: Preparation for Calculus

An exploration of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. This course is designed to prepare students for the study of calculus at Lawrence.
Units: 6.
Prerequisite: Minimum score on ALEKS diagnostic exam, as set by the department.

STAT 107: Principles of Statistics

For students in all disciplines. Provides the background needed to evaluate statistical arguments found in newspapers, magazines, reports, and journals and the logic and techniques necessary to perform responsible elementary statistical analysis. Topics include basic data analysis, one-variable regression, experimental and sampling design, random variables, sampling distributions, and inference (confidence intervals and significance testing). This course may not be taken on a Satisfactory/Unsatisfactory basis. Students with credit for MATH 140 or equivalent, or BIOL 170, or AP Statistics should not take this course and should instead consider STAT 255.
Units: 6.

MATH 120: Applied Calculus I

A course in the applications of mathematics to a wide variety of areas, stressing economics and the biological sciences. Topics may include recursive sequences and their equilibria, the derivative of a function, optimization, fitting abstract models to observed data. Emphasis placed on algebraic and numerical techniques and on understanding the role of mathematical thinking. Mathematics 120 and 130 do not prepare students for more advanced courses in mathematics.
Units: 6.
Prerequisite: Three years of high school mathematics;

MATH 130: Applied Calculus II

A continuation of math 120. Topics may include the indefinite and definite integral, elementary linear algebra including matrix arithmetic and solving linear equations, vectors, partial derivatives, Lagrange multipliers. Both algebraic and numerical computations.
Units: 6.
Prerequisite: MATH 120 or the equivalent

MATH 140: Calculus

Functions, limits, derivatives, the Mean Value Theorem, definition and properties of integrals, the Fundamental Theorem of Calculus, and applications to related rates, curve sketching, and optimization problems.
Units: 6.
Prerequisite: Minimum score on ALEKS online diagnostic exam, as set by the department.

MATH 155: Multivariable Calculus

Techniques of integration, vector algebra in the plane and space, matrix algebra, functions of several variables, partial derivatives, double and triple integration, optimization.
Units: 6.
Prerequisite: MATH 140 or suitable AP or IB score and minimum score on ALEKS online diagnostic exam as set by department

MATH 191: Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 200: Complex Sequences and Series

Complex numbers, sequences, convergence, series, power series, additional topics chosen from analysis, geometry, differential equations, and applied mathematics
Units: 6.
Prerequisite: MATH 155

STAT 205: Data-Scientific Programming

An introduction to programming with emphasis on learning from data in order to gain useful insights. Topics focus on elementary programming concepts in the R language and the necessary tools to handle, analyze and interpret data. This course will be taught in a workshop format, and students will complete regular assignments and a final project that provide hands-on programming/analysis experiences.
Units: 6.
Also listed as Computer Science 205
Prerequisite: One prior course MATH, STAT, or CMSC course, or BIOL 170, or consent of instructor

STAT 208: Machine Learning

An overview of techniques used to discover structural patterns and make predictions using complex datasets that are prevalent in today's world. The central machine learning tasks of classification, clustering, and regression will be explored, along with methods for training models and evaluating predictions. This course will be taught in a workshop format. Assignments will involve the use of statistical software.
Units: 6.
Also listed as Linguistics 208, Computer Science 208
Prerequisite: CMSC 150, or CMSC 205, or CMSC 210, or consent of instructor

MATH 210: Differential Equations with Linear Algebra

A study of differential equations and related techniques in linear algebra. Topics include first-order equations and their applications, existence and uniqueness of solutions, second-order linear equations and their applications, series solutions, systems of first-order equations, vector spaces and dimension, linear transformations, and eigenvalues.
Units: 6.
Prerequisite: MATH 200, or MATH 155 and consent of instructor; also PHYS 151

MATH 223: Quantitative Decision-Making

The students will learn how to develop formal, quantitative approaches to structuring difficult problems, particularly those problems involving probabilistic factors. We will develop and practice the steps of defining a problem, gathering data, formulating a model, performing numerical calculations, evaluating numerical information, refining the model, analyzing the model's alternatives, and communicating the results.
Units: 6.
Also listed as Economics 223
Prerequisite: Sophomore standing

MATH 230: Discrete Mathematics

An introduction to mathematical reasoning and proof in the context of discrete structures relevant to the study of computer science. Topics include induction, sets, relations and functions, graph theory, combinatorics, and probability.
Units: 6.
Prerequisite: MATH 155

MATH 250: Linear Algebra

The study of vector spaces, linear transformations, matrices, and applications. Topics include linear independence, dimension, rank-nullity, change of basis, eigenvectors and eigenvalues, determinants, and inner products.
Units: 6.
Prerequisite: MATH 200

STAT 255: Statistics for Data Science

This course introduces modern statistical techniques in the context of predictive inference and modeling. Topics will include data analysis techniques such as linear and logistic regression, ANOVA, nonparametric methods, and computational approaches such as cross-validation and bootstrapping. Statistical software will be used frequently. This class will involve regular in-class and out-of-class assignments as well as exams and quizzes.
Units: 6.
Prerequisite: STAT 107, BIOL 170, or MATH 140, or instructor permission

MATH 340: Probability

An introduction to probability and its applications. Topics will include combinatorial and axiomatic probability, conditional probability and Bayes' Theorem, random variables, expectation and variance, discrete and continuous probability distributions, joint and conditional distributions, and limit laws.
Units: 6.
Also listed as Statistics 340
Prerequisite: MATH 200, and either MATH 220 or MATH 230

STAT 340: Probability

An introduction to probability and its applications. Topics will include combinatorial and axiomatic probability, conditional probability and Bayes' Theorem, random variables, expectation and variance, discrete and continuous probability distributions, joint and conditional distributions, and limit laws.
Units: 6.
Also listed as Mathematics 340
Prerequisite: MATH 200, and either MATH 220 or MATH 230

MATH 350: Ordinary Differential Equations

A study of ordinary differential equations and applications. Topics include standard techniques for special types of equations, linear and non-linear systems, existence and uniqueness, and qualitative behavior.
Units: 6.
Prerequisite: MATH 250

MATH 390: Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

STAT 390: Tutorial Studies in Statistics

Advanced work in statistics on topics not covered in regular offerings.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 391: Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

STAT 391: Directed Study in Statistics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 395: Internship In Mathematics

The academic component of the internship includes readings related to the substance of the internship, discussions with the faculty supervisor, and a written report appropriate to the discipline. Course grades are based on this academic work.
Units: 1 TO 98.

MATH 399: Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 400: Partial Differential Equations

A survey of techniques used in modeling physical systems, with particular emphasis on partial differential equations and methods used to attack problems that do not have clean or simple solutions. Topics include techniques for solving partial differential equations exactly, the Fourier transform, perturbation theory, variational methods, Monte Carlo techniques, and finite difference schemes.
Units: 6.
Prerequisite: MATH 350

STAT 405: Advanced Data Computing

This course builds on CMSC/STAT 205, providing a deeper exploration of statistical computing in R. Topics might include efficient programming techniques, parallelization, statistical algorithms, advanced data visualization, and creation of R packages. Statistical software will be used extensively in this course. The class will be taught in an interactive lab-based format. There will be regular assignments and a project.
Units: 6.
Also listed as Computer Science 405
Prerequisite: CMSC 205

MATH 410: Linear Algebra

A study of vector spaces, linear transformations, and their representations. The focus will be on algebraic and coordinate-free methods, and topics will include dimension, dual spaces, determinants, canonical forms, inner product spaces, and the spectral theorem.
Units: 6.
Prerequisite: MATH 300

MATH 420: Numerical Analysis

Computer approximated (numerical) solutions to a variety of problems with an emphasis on error analysis. Interpolation, evaluation of polynomials and series, solution of linear and non-linear equations, eigenvectors, quadrature (integration), and differential equations.
Units: 6.
Prerequisite: MATH 250, one CMSC (computer science) course recommended

MATH 435: Optimization

The study of local and global maximums and minimums of function, given various sorts of constraints. Linear problems and the simplex algorithm, general non-linear problems and the Kuhn-Tucker conditions, convex problems. Perturbation of problem parameters and duality. Applications to a wide variety of fields, including economics, game theory, and operations research.
Units: 6.
Prerequisite: MATH 230 and 250, or MATH 310

MATH 445: Mathematical Statistics

Development of the mathematical theory of statistics and its application to the real world. The course will focus on the principles of estimation and testing from both the frequentist and Bayesian perspectives. Resampling methods (permutation tests and bootstrap intervals) will also be explored.
Units: 6.
Prerequisite: MATH/STAT 340

STAT 445: Mathematical Statistics

Development of the mathematical theory of statistics and its application to the real world. The course will focus on the principles of estimation and testing from both the frequentist and Bayesian perspectives. Resampling methods (permutation tests and bootstrap intervals) will also be explored.
Units: 6.
Prerequisite: MATH/STAT 340

STAT 450: Bayesian Statistics

A study of the Bayesian statistical philosophy, contrasting it with the traditional frequentist approach taught in other statistics courses. Topics include Bayes' Theorem, prior and posterior probability distributions, hierarchical models, and Markov Chain Monte Carlo methods. The course will involve a mixture of lecture, discussion, and use of statistical software. Requirements include exams, a project, and assignments involving the use of statistical software.
Units: 6.
Prerequisite: MATH/STAT 340

STAT 455: Advanced Statistical Modeling

This course expands on STAT 255, and introduces more sophisticated models, meant to capture complicated correlation structure in data. Topics might include generalized linear models, mixed-effects models, hierarchical models, spatial models, and time series. The course will involve the use of statistical software. There will be regular assignments, exams, and possibly projects.
Units: 6.
Prerequisite: STAT 255 or instructor permission

MATH 510: Real Analysis

A study of concepts in mathematical analysis, including convergence of sequences and series, continuity, differentiation, integration, and metric spaces.
Units: 6.
Prerequisite: MATH 230 and MATH 250

MATH 525: Graph Theory

A survey of graph theory that balances the abstract theory of graphs with a wide variety of algorithms and applications to “real world” problems. Topics include trees, Euler tours and Hamilton cycles, matchings, colorings, directed graphs, and networks.
Units: 6.
Prerequisite: MATH 230 and 250, or MATH 300

MATH 530: Topics in Geometry

The axiomatic development of euclidean and non-euclidean geometry, including the historical and philosophical issues raised by the “non-euclidean revolution.” Additional topics, such as projective or differential geometry and convexity, may be included.
Units: 6.
Prerequisite: MATH 230 and MATH 250, or MATH 300

MATH 535: Complex Analysis

An introduction to functions of a complex variable, the Cauchy-Riemann equations, conformal mappings, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, and a sampling, as time and interest permit, of the corollaries to Cauchy’s theorem.
Units: 6.
Prerequisite: MATH 230 and 250

MATH 545: Rings and Fields

Modern algebra with topics selected from group theory, ring theory, field theory, classical geometric construction problems, and Galois theory. Emphasis on the use of mathematical abstraction to illuminate underlying relationships and structure.
Units: 6.
Prerequisite: MATH 230 and 250

MATH 550: Topics in Analysis

Selected topics in analysis covering a wide variety of spaces and leading to applications of classical importance. In recent years, topics have included fixed point theory, inverse and implicit function theorems, abstract theory of differential equations, Lebesgue measure and integration, Fourier series and transforms.
Units: 6.
Prerequisite: MATH 310

MATH 555: Topics in Algebra and Combinatorics

A study of interconnections between abstract algebra (especially finite group theory) and combinatorics (especially graph theory). Topics will include classical results (such as the matrix-tree theorem), as well as recent subjects and advances (such as the abelian sandpile model and the Riemann-Roch theorem for graphs).
Units: 6.
Prerequisite: MATH 230 and MATH 250

MATH 560: Topology

A study of metric and topological spaces, including continuity, compactness, connectedness, product and quotient spaces. Additional topics may include Zorn’s Lemma, separation properties, surfaces, the fundamental group, and fixed point theorems.
Units: 6.
Prerequisite: MATH 230 and 250

MATH 565: Number Theory

A study of the integers, including unique factorization, congruences, and quadratic reciprocity. Other topics may include finite fields, higher reciprocity laws, and algebraic number theory.
Units: 6.
Prerequisite: MATH 230 and 250

MATH 590: Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

STAT 590: Tutorial Studies in Statistics

Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 591: Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

STAT 591: Directed Study in Statistics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 599: Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 600: History of Mathematics

A study of the history of mathematics from the ancient Greeks through the present, emphasizing the role of mathematics in scientific advances, the work of great mathematicians, and the modern branching of the subject into a multitude of specialties.
Units: 6.
Prerequisite: MATH 310

MATH 690: Tutorial Studies in Mathematics

Advanced work in mathematics on topics not covered in regular offerings.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 691: Directed Study in Mathematics

Directed study follows a syllabus set primarily by the instructor to meet the needs or interests of an individual student or small group of students. The main goal of directed study is knowledge or skill acquisition, not research or creative work.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

MATH 699: Independent Study in Mathematics

Guided independent study of an advanced topic in undergraduate mathematics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.

STAT 699: Independent Study in Statistics

Guided independent study of an advanced topic in undergraduate statistics or supervised work on an undergraduate research project, generally culminating in a final presentation and/or paper.
Units: 1 TO 98.
Prerequisite: Counter Registration Required.