Please consult Is There Life After Calculus? for assistance in selecting an appropriate course. Course descriptions are included below.
MATH 3040 - Prove It!
Fall 2026, Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
A useful course for students who wish to improve their skills in mathematical proof and exposition, or who intend to study more advanced topics in mathematics. The methodology of proof provides a central tool for confirming the validity of mathematical assertions, functioning much as the experimental method does in the physical sciences. We will study various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and in set theory and combinatorics, then moving to applications and illustrations of these via topics in one or more of the three main pillars of mathematics: algebra, analysis, and geometry. Because cogent communication of mathematical ideas is important in the presentation of proofs, the course emphasizes clear, concise exposition.
MATH 3110 - Introduction to Analysis
Fall 2026, Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 3110, MATH 4130
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Provides a transition from calculus to real analysis. Topics include rigorous treatment of fundamental concepts in calculus: including limits and convergence of sequences and series, compact sets; continuity, uniform continuity and differentiability of functions. Emphasis will be placed upon understanding and constructing mathematical proofs.
MATH 3210 - Manifolds and Differential Forms
Fall 2026. 4 credits. Student option grading.
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
A manifold is a type of subset of Euclidean space that has a well-defined tangent space at every point. Such a set is amenable to the methods of multivariable calculus. After reviewing some relevant calculus, this course investigates manifolds and the structures they are endowed with, such as tangent vectors, boundaries, orientations, and differential forms. The notion of a differential form encompasses such ideas as area forms and volume forms, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space or hyperspace. We re-examine the integral theorems of vector calculus (Green, Gauss, and Stokes) in the light of differential forms and apply them to problems in partial differential equations, topology, fluid mechanics, and electromagnetism.
MATH 3270 - Introduction to Ordinary Differential Equations
Fall 2026. 3 credits. Student option grading.
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
A one-semester introduction to the theory and techniques of ordinary differential equations. Topics may include first-order and second-order differential equations, systems of linear differential equations, initial-value and two-point boundary-value problems, Sturm-Liouville theory, Sturm oscillation and comparison theory, the basic existence and uniqueness theorems, series solutions, special functions, and Laplace transforms. Applications from science and engineering may be included at the instructor’s discretion.
MATH 3320 - Introduction to Number Theory
Fall 2026, Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
An introductory course on number theory, the branch of algebra that studies the deeper properties of integers and their generalizations. Usually includes most of the following topics: the Euclidean algorithm, continued fractions, Pythagorean triples, Diophantine equations such as Pell’s equation, congruences, quadratic reciprocity, binary quadratic forms, Gaussian integers, and factorization in quadratic number fields. May include a brief introduction to Fermat’s Last Theorem.
MATH 3340 - Abstract Algebra
Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 3340 and MATH 3360, nor for both MATH 3340 and MATH 4340.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
An introduction to structures of abstract algebra, including groups, rings, fields, factorization of polynomials and integers, congruences, and the structure of finite abelian groups. Additional topics include modules over Euclidean domain and Sylow theorems. Students considering graduate school in mathematics might consider taking MATH 4330 after MATH 3340.
MATH 3360 - Applicable Algebra
Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 3340, MATH 3360
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Introduction to the concepts and methods of abstract algebra and number theory that are of interest in applications. Covers the basic theory of groups, rings, and fields and their applications to such areas as public-key cryptography, error-correcting codes, parallel computing, and experimental designs. Applications include the RSA cryptosystem and use of finite fields to construct error-correcting codes and Latin squares. Topics include elementary number theory, Euclidean algorithm, prime factorization, congruences, theorems of Fermat and Euler, elementary group theory, Chinese remainder theorem, factorization in the ring of polynomials, and classification of finite fields.
MATH 3610 - Mathematical Modeling
Fall 2026. 4 credits. Student option grading.
Prerequisites: MATH 1110-MATH 1120 or equivalent.
Introduction to the theory and practice of mathematical modeling. We compare and contrast different types of mathematical models (discrete vs. continuous, deterministic vs. stochastic), focusing on advantages, disadvantages, and limits of applicability for each approach. Case-study format covers a variety of application areas including economics, physics, sociology, traffic engineering, urban planning, robotics, and resource management. Students learn how to implement mathematical models on the computer and how to interpret/describe the results of their computational experiments.
MATH 3810 - Deductive Logic
Crosslisted with PHIL 3310, COGST 3310; Co-meets with PHIL 6310
Spring 2026. 4 credits. Student option grading.
Prerequisites: PHIL 2310 or MATH 2210 or MATH 2230 or permission of instructor.
A mathematical study of the formal languages of standard first-order propositional and predicate logic, including their syntax, semantics, and deductive systems. The basic apparatus of model theory will be presented. Various formal results will be established, most importantly soundness and completeness.
MATH 3840 - Introduction to Set Theory
Crosslisted with PHIL 3300; Co-meets with PHIL 6311
3 credits. Student option grading.
This will be a course on standard set theory (first developed by Ernst Zermelo early in the 20th century): the basic concepts of sethood and membership, operations on sets, functions as sets, the set-theoretic construction of the Natural Numbers, the Integers, the Rational and Real numbers; time permitting, some discussion of cardinality. Course was formerly titled “Foundations of Mathematics”.
MATH 3850 - Modal Logic
Crosslisted with PHIL 3340
3 credits. Student option grading.
Prerequisites: PHIL 2310 or equivalent.
Modal logic is a general logical framework for systematizing reasoning about qualified and relativized truth. It has been used to study the logic of possibility, time, knowledge, obligation, provability, and much more. This course will explore both the theoretical foundations and the various philosophical applications of modal logic. On the theoretical side, we will cover basic metatheory, including Kripke semantics, soundness and completeness, correspondence theory, and expressive power. On the applied side, we will examine temporal logic, epistemic logic, deontic logic, counterfactuals, two-dimensional logics, and quantified modal logic.
MATH 4030 - History of Mathematics
Not offered 2026-2027. 4 credits. Student option grading.
Prerequisites: two mathematics courses above 3000, or permission of instructor.
Development of mathematics from Babylon and Egypt and the Golden Age of Greece through its nineteenth century renaissance in the Paris of Cauchy and Lagrange and the Berlin of Weierstrass and Riemann. Covers basic algorithms underlying algebra, analysis, number theory, and geometry in historical order. Theorems and exercises cover the impossibility of duplicating cubes and trisecting angles, which regular polygons can be constructed by ruler and compass, the impossibility of solving the general fifth degree algebraic equation by radicals, and the transcendence of pi. Students will be expected to be comfortable writing proofs and will give presentations from original sources over 5000 years of mathematics.
MATH 4040 - Patterns, Proofs, and Problems
Fall 2026. 4 credits. Student option grading.
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Basic problem-solving techniques and strategies for contest problems. Contest problems differ from standard mathematical instruction in that they are "contextless": the problem does not tell you which field it is in, and sometimes goes to great lengths to disguise it. Understanding how to solve contest problems is useful not only in contest participation, but also in research, where knowing how to work with unknown concepts, how to attack a problem fluidly from the perspective of multiple fields, and different tricks for simplifying problems is extremely useful. This course will cover all of the topics that may appear in standard competitions (such as the Putnam exam), including combinatorics, number theory, geometry, and calculus. It will also teach strategies for understanding and attacking problems, more advanced proof techniques, and effective proof writing.
MATH 4130 - Honors Introduction to Analysis I
Fall 2026, Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 3110, MATH 4130
Prerequisites: high level of performance in a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Introduction to the rigorous theory underlying calculus, covering the real number system and functions of one variable. Topics typically include construction of the real number system, properties of the real number system, continuous functions, differential and integral calculus of functions of one variable, sequences and series of functions. Based entirely on proofs. The student is expected to know how to read and, to some extent, construct proofs before taking this course. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4140 - Honors Introduction to Analysis II
Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 4130.
A proof-based introduction to further topics in analysis. Topics may include the Lebesgue measure and integration, functions of several variables, differential calculus, implicit function theorem, infinite dimensional normed and metric spaces, Fourier series, and ordinary differential equations.
MATH 4180 - Complex Analysis
Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 4180, MATH 4220
Prerequisites: MATH 2230-MATH 2240, MATH 3110, or MATH 4130, or permission of instructor.
A theoretical and rigorous introduction to complex variable theory recommended for students who plan to attend graduate school in mathematics. Topics include complex numbers, differential and integral calculus for functions of a complex variable, including Cauchy's theorem and the calculus of residues, elements of conformal mapping. Students will be expected to be comfortable writing proofs. For applications of complex analysis, consider MATH 4220 rather than MATH 4180.
MATH 4200 - Differential Equations and Dynamical Systems
Spring 2027. 3 credits. Student option grading.
Forbidden Overlaps: MAE 5790, MATH 4200, MATH 4210, MATH 5200
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Covers ordinary differential equations in one and higher dimensions: qualitative, analytic, and numerical methods. Emphasis is on differential equations as models and the implications of the theory for the behavior of the system being modeled and includes an introduction to bifurcations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4210 - Nonlinear Dynamics and Chaos
Fall 2026. 3 credits. Student option grading.
Forbidden Overlaps: MAE 5790, MATH 4200, MATH 4210, MATH 5200
Prerequisites: high level of performance in a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Recommended prerequisite: MATH 2930 or equivalent preparation in differential equations.
An introduction to nonlinear dynamics with applications to physics, engineering, biology, and chemistry. Emphasizes analytical methods, concrete examples, and geometric thinking. Topics include one-dimensional systems; bifurcations; phase plane; nonlinear oscillators; and Lorenz equations, chaos, strange attractors, fractals, iterated mappings, period doubling, renormalization. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4220 - Applied Complex Analysis
Fall 2026. 3 credits. Student option grading.
Forbidden Overlaps: MATH 4180, MATH 4220, MATH 5220
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Covers complex variables, Fourier transforms, Laplace transforms and applications to partial differential equations. Additional topics may include an introduction to generalized functions. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Undergraduates who plan to attend graduate school in mathematics should take MATH 4180 rather than MATH 4220.
MATH 4250 - Numerical Analysis and Differential Equations
Crosslisted with CS 4210
Fall 2026. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230-MATH 2240, MATH 2310, or MATH 2940 or equivalent and one additional mathematics course numbered 3000 or above.
Introduction to the fundamentals of numerical analysis: error analysis, approximation, interpolation, and numerical integration. In the second half of the course, we use these to build approximate solvers for ordinary and partial differential equations. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is used to test the theoretical concepts throughout the course. Students will be expected to be comfortable writing proofs and have knowledge of programming. MATH 4250/CS 4210 and MATH 4260/CS 4220 can be taken independently from each other and in either order. Together they provide a comprehensive introduction to numerical analysis.
MATH 4260 - Numerical Analysis: Linear and Nonlinear Problems
Crosslisted with CS 4220
Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 2210 or MATH 2940 or equivalent.
Introduction to the fundamentals of numerical linear algebra: direct and iterative methods for linear systems, eigenvalue problems, singular value decomposition. In the second half of the course, the above are used to build iterative methods for nonlinear systems and for multivariate optimization. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is required to test the theoretical concepts throughout the course.
MATH 4280 - Introduction to Partial Differential Equations
Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 2930, MATH 3270, or equivalent.
Topics are selected from first-order quasilinear equations, classification of second-order equations, with emphasis on maximum principles, existence, uniqueness, stability, and Fourier series methods. Additional topics as time permits. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4310 - Linear Algebra
Fall 2026, Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 4310, MATH 4330
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Introduction to linear algebra, including the study of vector spaces, linear transformations, matrices, and systems of linear equations. Additional topics include quadratic forms and inner product spaces, canonical forms for various classes of matrices and linear transformations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Undergraduates who plan to attend graduate school in mathematics should take MATH 4330 instead of MATH 4310.
MATH 4330 - Honors Linear Algebra
Fall 2026. 4 credits. Student option grading.
Forbidden Overlaps: MATH 4310, MATH 4330
Prerequisites: high level of performance in MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Honors version of a course in advanced linear algebra, which treats the subject from an abstract and axiomatic viewpoint. Topics include vector spaces, linear transformations, polynomials, determinants, tensor and wedge products, canonical forms, inner product spaces, and bilinear forms. Emphasis is on understanding the theory of linear algebra; homework and exams include at least as many proofs as computational problems. Strong proficiency in writing proofs is expected. More experience with proofs may be gained by first taking a 3000-level MATH course. MATH 4330-MATH 4340 is recommended for undergraduates who plan to attend graduate school in mathematics. For a less theoretical course that covers approximately the same subject matter as MATH 4330, see MATH 4310.
MATH 4340 - Honors Introduction to Algebra
Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: MATH 3340, MATH 4340
Prerequisites: MATH 4330.
Honors version of a course in abstract algebra, which treats the subject from an abstract and axiomatic viewpoint, including universal mapping properties. Topics include groups, groups acting on sets, Sylow theorems; rings, Euclidean domains, factorization, structure theorem of finitely generated modules over a principal ideal domain; fields, root adjunction, finite fields, introduction to Galois theory. The course emphasizes understanding the theory with proofs in both homework and exams. MATH 4330-MATH 4340 is recommended for undergraduates who plan to attend graduate school in mathematics. For a less theoretical course that covers subject matter similar to MATH 4340, see MATH 3340.
MATH 4370 - Computational Algebra
Fall 2026. 3 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Introduction to algebraic geometry and computational algebra. Students will learn how to compute a Gröbner basis for polynomials in many variables. Covers the following applications: solving systems of polynomial equations in many variables, solving diophantine equations in many variables, 3-colorable graphs, and integer programming. Such applications arise, for example, in computer science, engineering, economics, and physics. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4410 - Introduction to Combinatorics I
Fall 2026. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Combinatorics studies discrete structures arising in mathematics, computer science, and many areas of application. Key topics include counting objects with specific properties (e.g., trees) and proving the existence of structures (e.g., matchings of all vertices in a graph). We cover basic questions in graph theory, including extremal graph theory (how large a graph must be to have a certain subgraph) and Ramsey theory (large objects are forced to have structure). An introduction to network flow theory and variations on matching theory, including theorems of Dilworth, Hall, König, and Birkhoff, are discussed. Methods of enumeration (inclusion/exclusion, Möbius inversion, and generating functions) are applied to problems of counting permutations, partitions, and triangulations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4420 - Introduction to Combinatorics II
Not offered 2026-2027. Expected Spring 2027. 4 credits. Student option grading.
Prerequisite: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Continuation of MATH 4410, although formally independent of the material covered there. The emphasis here is the study of certain combinatorial structures, such as Latin squares and combinatorial designs (which are of use in statistical experimental design), classical finite geometries and combinatorial geometries (also known as matroids, which arise in many areas from algebra and geometry through discrete optimization theory). We introduce partially ordered sets and lattices, including general Möbius inversion and its application, as well as the Polya theory of counting in the presence of symmetries. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4500 - Matrix Groups
Spring 2027. 4 credits. Student option grading.
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Matrix groups are central to mathematics and important in physics and engineering. The objects of study are classes of matrices (e.g., orthogonal, unitary, or symplectic) with both algebraic (groups) and geometric/topological (manifolds) structure. Thus the course is a mixture of algebra, geometry/topology, and a little analysis. Topics include Lie algebras (an extension of the notion of vector multiplication in three-dimensional space), the exponential mapping (a generalization of the exponential function of calculus), and representation theory (which studies different ways groups can be represented by matrices). Concrete examples will be emphasized. Background not included in the prerequisites will be developed as needed. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4520 - Classical Geometries and Modern Applications
Not offered 2026-2027. Expected Fall 2027. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
An introduction to projective, hyperbolic, and spherical geometry and their modern applications. The course will be divided into short modules with an emphasis on participation, discovery, and student projects and presentations. In addition to proving theorems, students will have the opportunity to make, build, 3D print, or program something related to the course material as a project component. We will cover classical theorems and techniques (e.g., stereographic projection and conics) and see how classical geometry is used in and relates to other areas of mathematics (e.g., topology, via Euler characteristic) and applications such as computer vision, networks, or architectural drawing. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4530 - Introduction to Topology
Fall 2026. 4 credits. Student option grading.
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Topology may be described briefly as qualitative geometry. This course begins with basic point-set topology, including connectedness, compactness, and metric spaces. Later topics may include the classification of surfaces (such as the Klein bottle and Möbius band), elementary knot theory, or the fundamental group and covering spaces. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4540 - Introduction to Differential Geometry
Spring 2027. 4 credits. Student option grading.
Prerequisites: a semester of linear algebra (MATH 2210, MATH 2230, MATH 2310, or MATH 2940) and a semester of multivariable calculus (MATH 2220, MATH 2240, or MATH 1920), or equivalent.
Differential geometry involves using calculus to study geometric concepts such as curvature and geodesics. This introductory course focuses on the differential geometry of curves and surfaces. It may also touch upon the higher-dimensional generalizations, Riemannian manifolds, which underlie the study of general relativity. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4710 - Basic Probability
Fall 2026, Spring 2027. 4 credits. Student option grading.
Forbidden Overlaps: ECON 3110, ECON 3130, ILRST 3080, ILRST 3110, MATH 4710, STSCI 3080, STSCI 3110
Prerequisites: MATH 1110-MATH 1120, or equivalent.
Recommended prerequisite: MATH 1920, MATH 2220, or equivalent.
An introduction to probability theory that prepares the student to take MATH 4720. The course begins with basics: combinatorial probability, mean and variance, independence, conditional probability, and Bayes formula. Density and distribution functions and their properties are introduced. The law of large numbers and central limit theorem are stated and their implications for statistics are discussed.
MATH 4720 - Theory of Statistics
Crosslisted with STSCI 4090
Fall 2026, Spring 2027. 4 credits. Letter grades only.
Prerequisites: STSCI 3080 or MATH 4710 or equivalent and at least one introductory statistics course.
Introduction to classical theory of parametric statistical inference that builds on the material covered in STSCI 3080. Topics include: sampling distributions, principles of data reduction, likelihood, parameter estimation, hypothesis testing, interval estimation, and basic asymptotic theory.
MATH 4740 - Stochastic Processes
Spring 2027. 4 credits. Student option grading.
Prerequisites: MATH 4710, ILRST/STSCI 3080, ORIE 3500, or ECON 3130 and linear algebra (MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent).
A one-semester introduction to stochastic processes which develops the theory together with applications. Covers Markov chains in discrete and continuous time and Poisson processes. Other topics may include queuing theory, martingales, Brownian motion, and option pricing. This course may be useful to graduate students in the biological sciences or other disciplines who encounter stochastic models in their work but who do not have the background for more advanced courses such as ORIE 6500. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4810 - Mathematical Logic
(also PHIL 4310)
Fall 2026. 4 credits. Student option grading.
Forbidden Overlaps: CS 4860, MATH 4810, MATH 4860, PHIL 4310
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
First course in mathematical logic providing precise definitions of the language of mathematics and the notion of proof (propositional and predicate logic). The completeness theorem says that we have all the rules of proof we could ever have. The Gödel incompleteness theorem says that they are not enough to decide all statements even about arithmetic. The compactness theorem exploits the finiteness of proofs to show that theories have unintended (nonstandard) models. Possible additional topics: the mathematical definition of an algorithm and the existence of noncomputable functions; the basics of set theory to cardinality and the uncountability of the real numbers. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking CS 2800 or a 3000-level MATH course.
MATH 4820 - Topics in Logic and the Foundations of Mathematics
Crosslisted with PHIL 4311
Not offered 2026-2027. 3 credits. Student option grading.
Prerequisites: PHIL 2310, PHIL 3310, PHIL 3300, MATH 3840, or permission of instructor. A background in logic is required.
Advanced discussion of a topic in logic or foundational mathematics.
MATH 4860 - Applied Logic
Crosslisted with CS 4860
Not offered 2026-2027. 3 credits. Student option grading.
Forbidden Overlaps: CS 4860, MATH 4810, MATH 4860, PHIL 4310
Prerequisites: MATH 2210, MATH 2230, MATH 2310, MATH 2940, or equivalent.
Topics chosen from propositional logic, first-order logic, and higher-order logic, both classical and intuitionistic versions, including completeness, incompleteness, and compactness results. Natural deduction and tableaux style logics and connection to the lambda calculus and programming languages and logics, and program verification. Other topics chosen from equational logic, Herbrand universes and unification, rewrite rules and Knuth-Bendix method, and the congruence-closure algorithm and lambda-calculus reduction strategies. Modal logics, intuitionistic logic, computational logics and programming languages (e.g., LISP, ML, or Nuprl). Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.
MATH 4870 - Set Theory
Crosslisted with PHIL 4300
3 credits. Student option grading.
Prerequisites: at least one prior course in Philosophy or logic, or permission of instructor.
This course is a sequel to PHIL 3300/MATH 3840 but is also open to students who have not had the latter. After a brief review of the central ideas from the latter course, it will cover the construction of the real numbers, cardinality, the ordinal numbers, the cardinal numbers, the axiom of choice, and time permitting, another topic or two.
MATH 4900 - Supervised Research
Fall 2026, Spring 2027. 1-4 credits, variable. Student option grading.
Permission of instructor required. To apply for independent study, please complete the on-line form.
An independent research course by arrangement with an individual professor. The goal is for the student to perform an independent investigation into a specific mathematical question. The student and professor will set expectations and grading policies at the beginning of the term.
MATH 4901 - Supervised Reading
Fall 2026, Spring 2027. 1-4 credits, variable. Student option grading.
Permission of instructor required. To apply for independent study, please complete the on-line form.
An independent reading course by arrangement with an individual professor. The goal is for the student to master a body of mathematics outside the normal curriculum. The student and professor will set expectations and grading policies at the beginning of the term.
MATH 4980 - Special Study for Mathematics Teaching
Not offered 2026-2027. 1-3 credits, variable. Student option grading.
Permission of instructor required.
Examines principles underlying the content of the secondary school mathematics curriculum, including connections with the history of mathematics, technology, and mathematics education research. One credit is awarded for attending two Saturday workshops (see e.math.cornell.edu/classes/math5080) and writing a paper. Other credit options are available for students completing additional work, such as tutoring at a local middle school or completing a research paper or project. Does not count toward the math major or math minor and will not count as degree credits for A&S students.
MATH 4997 - Practical Training in Mathematics
Fall 2026. 1 credit. S/U grades only (no audit).
Primarily for: international undergraduate math majors whose application to affiliate has been approved. Permission of department required.
This independent study course offers math majors (i.e., undergraduates whose applications to affiliate with the math major have been approved) an opportunity to reflect on concepts from mathematics as they were encountered and applied in a recent internship. Students write a short paper describing their work experience and how it connects to the educational objectives of the mathematics major.