# Mathematics Courses of Instruction

## Mathematics Courses of Instruction

**MATH UN1003 COLLEGE ALGEBRA-ANLYTC GEOMTRY.** *3.00 points*.

Prerequisites: score of 550 on the mathematics portion of the SAT completed within the last year, or the appropriate grade on the General Studies Mathematics Placement Examination. For students who wish to study calculus but do not know analytic geometry. Algebra review, graphs and functions, polynomial functions, rational functions, conic sections, systems of equations in two variables, exponential and logarithmic functions, trigonometric functions and trigonometric identities, applications of trigonometry, sequences, series, and limits. This course may not be taken for credit after the successful completion of any course in the Calculus sequence

Fall 2024: MATH UN1003 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1003 | 001/00010 | M W 6:10pm - 7:25pm 323 Milbank Hall |
Lindsay Piechnik | 3.00 | 52/56 |

Spring 2025: MATH UN1003 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1003 | 001/15269 | M W 11:40am - 12:55pm Room TBA |
3.00 | 0/30 | |

MATH 1003 | 002/15270 | T Th 6:10pm - 7:25pm Room TBA |
3.00 | 0/30 |

**MATH UN1101 CALCULUS I.** *3.00 points*.

Prerequisites: (see Courses for First-Year Students). Functions, limits, derivatives, introduction to integrals, or an understanding of pre-calculus will be assumed. (SC)

Fall 2024: MATH UN1101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1101 | 001/00081 | T Th 1:10pm - 2:25pm 263 Macy Hall |
Lindsay Piechnik | 3.00 | 98/100 |

MATH 1101 | 002/00082 | Th 2:40pm - 3:55pm 405 Milbank Hall |
Lindsay Piechnik | 3.00 | 98/100 |

MATH 1101 | 003/11833 | M W 10:10am - 11:25am 203 Mathematics Building |
Marco Castronovo | 3.00 | 50/100 |

MATH 1101 | 004/11835 | M W 11:40am - 12:55pm 203 Mathematics Building |
Marco Castronovo | 3.00 | 66/100 |

MATH 1101 | 005/11837 | M W 2:40pm - 3:55pm 312 Mathematics Building |
George Dragomir | 3.00 | 93/106 |

MATH 1101 | 006/11838 | M W 4:10pm - 5:25pm 703 Hamilton Hall |
Alex Scheffelin | 3.00 | 29/30 |

MATH 1101 | 007/11840 | M W 6:10pm - 7:25pm 207 Mathematics Building |
Marco Sangiovanni Vincentelli | 3.00 | 19/100 |

MATH 1101 | 008/11841 | T Th 10:10am - 11:25am 520 Mathematics Building |
Soren Galatius | 3.00 | 43/45 |

MATH 1101 | 009/11842 | T Th 11:40am - 12:55pm 142 Uris Hall |
George Dragomir | 3.00 | 107/108 |

MATH 1101 | 010/11844 | T Th 4:10pm - 5:25pm 142 Uris Hall |
Marco Sangiovanni Vincentelli | 3.00 | 24/100 |

MATH 1101 | 011/11845 | T Th 6:10pm - 7:25pm 407 Mathematics Building |
Matthew Hase-Liu | 3.00 | 31/30 |

MATH 1101 | 012/00857 | M W 1:10pm - 2:25pm 152 Horace Mann Hall |
Wenjian Liu | 3.00 | 38/60 |

Spring 2025: MATH UN1101 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1101 | 001/00472 | M W 1:10pm - 2:25pm 263 Macy Hall |
Dusa McDuff | 3.00 | 0/90 |

MATH 1101 | 002/15277 | M W 4:10pm - 5:25pm Room TBA |
3.00 | 0/30 | |

MATH 1101 | 003/15278 | M W 6:10pm - 7:25pm Room TBA |
Brian Harvie | 3.00 | 0/100 |

MATH 1101 | 004/15280 | T Th 10:10am - 11:25am Room TBA |
Roger Van Peski | 3.00 | 0/100 |

MATH 1101 | 005/15281 | T Th 1:10pm - 2:25pm Room TBA |
Roger Van Peski | 3.00 | 0/100 |

MATH 1101 | 006/15282 | T Th 4:10pm - 5:25pm Room TBA |
3.00 | 0/30 |

**MATH UN1102 CALCULUS II.** *3.00 points*.

Prerequisites: MATH UN1101 or the equivalent.

Prerequisites: MATH UN1101 or the equivalent. Methods of integration, applications of the integral, Taylors theorem, infinite series. (SC)

Fall 2024: MATH UN1102 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1102 | 001/11847 | M W 1:10pm - 2:25pm 207 Mathematics Building |
Andres Ibanez Nunez | 3.00 | 89/100 |

MATH 1102 | 002/11848 | M W 2:40pm - 3:55pm 207 Mathematics Building |
Andres Ibanez Nunez | 3.00 | 54/100 |

MATH 1102 | 004/11850 | T Th 8:40am - 9:55am 203 Mathematics Building |
Lucy Yang | 3.00 | 48/100 |

MATH 1102 | 005/11851 | T Th 10:10am - 11:25am 203 Mathematics Building |
Lucy Yang | 3.00 | 43/100 |

MATH 1102 | 006/11852 | T Th 6:10pm - 7:25pm 417 Mathematics Building |
Elliott Stein | 3.00 | 63/64 |

Spring 2025: MATH UN1102 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1102 | 001/00477 | T Th 2:40pm - 3:55pm Ll002 Milstein Center |
Lindsay Piechnik | 3.00 | 0/90 |

MATH 1102 | 002/15285 | M W 10:10am - 11:25am Room TBA |
Evan Sorensen | 3.00 | 0/100 |

MATH 1102 | 003/00493 | M W 11:40am - 12:55pm 263 Macy Hall |
0. FACULTY | 3.00 | 0/100 |

MATH 1102 | 004/15287 | M W 4:10pm - 5:25pm Room TBA |
3.00 | 0/30 | |

MATH 1102 | 005/15289 | T Th 10:10am - 11:25am Room TBA |
Peter Woit | 3.00 | 0/64 |

MATH 1102 | 006/15291 | T Th 11:40am - 12:55pm Room TBA |
Dawei Shen | 3.00 | 0/30 |

MATH 1102 | 007/15294 | T Th 1:10pm - 2:25pm Room TBA |
Andres Ibanez Nunez | 3.00 | 0/100 |

**MATH UN1201 CALCULUS III.** *3.00 points*.

Prerequisites: MATH UN1101 or the equivalent

Prerequisites: MATH UN1101 or the equivalent Vectors in dimensions 2 and 3, complex numbers and the complex exponential function with applications to differential equations, Cramers rule, vector-valued functions of one variable, scalar-valued functions of several variables, partial derivatives, gradients, surfaces, optimization, the method of Lagrange multipliers. (SC)

Fall 2024: MATH UN1201 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1201 | 001/00011 | M W 10:10am - 11:25am 504 Diana Center |
Wenjian Liu | 3.00 | 63/70 |

MATH 1201 | 002/11853 | M W 8:40am - 9:55am 312 Mathematics Building |
Deeparaj Bhat | 3.00 | 57/100 |

MATH 1201 | 003/11854 | M W 11:40am - 12:55pm 312 Mathematics Building |
Brian Harvie | 3.00 | 97/100 |

MATH 1201 | 004/11855 | M W 2:40pm - 3:55pm 203 Mathematics Building |
Brian Harvie | 3.00 | 89/100 |

MATH 1201 | 005/11856 | T Th 11:40am - 12:55pm 203 Mathematics Building |
Gyujin Oh | 3.00 | 98/100 |

MATH 1201 | 006/11857 | T Th 1:10pm - 2:25pm 207 Mathematics Building |
Gyujin Oh | 3.00 | 101/100 |

MATH 1201 | 007/11861 | T Th 2:40pm - 3:55pm 207 Mathematics Building |
Yoonjoo Kim | 3.00 | 88/100 |

MATH 1201 | 008/11862 | T Th 4:10pm - 5:25pm 312 Mathematics Building |
Yoonjoo Kim | 3.00 | 82/100 |

Spring 2025: MATH UN1201 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1201 | 001/00494 | M W 10:10am - 11:25am 263 Macy Hall |
Cristian Iovanov | 3.00 | 0/90 |

MATH 1201 | 002/00496 | M W 11:40am - 12:55pm 405 Milbank Hall |
Cristian Iovanov | 3.00 | 0/90 |

MATH 1201 | 003/15298 | M W 2:40pm - 3:55pm Room TBA |
Deeparaj Bhat | 3.00 | 0/100 |

MATH 1201 | 004/15300 | T Th 1:10pm - 2:25pm Room TBA |
Deeparaj Bhat | 3.00 | 0/100 |

MATH 1201 | 005/15301 | T Th 4:10pm - 5:25pm Room TBA |
Rostislav Akhmechet | 3.00 | 0/100 |

MATH 1201 | 006/15302 | T Th 6:10pm - 7:25pm Room TBA |
Rostislav Akhmechet | 3.00 | 0/100 |

**MATH UN1202 CALCULUS IV.** *3.00 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent Multiple integrals, Taylor's formula in several variables, line and surface integrals, calculus of vector fields, Fourier series. (SC)

Fall 2024: MATH UN1202 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1202 | 001/00012 | M W 10:10am - 11:25am Ll001 Milstein Center |
Daniela De Silva | 3.00 | 38/50 |

MATH 1202 | 002/11863 | M W 6:10pm - 7:25pm 203 Mathematics Building |
Mikhail Smirnov | 3.00 | 52/100 |

Spring 2025: MATH UN1202 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 1202 | 001/15304 | M W 4:10pm - 5:25pm Room TBA |
Ovidiu Savin | 3.00 | 0/64 |

MATH 1202 | 002/15306 | T Th 2:40pm - 3:55pm Room TBA |
Marco Sangiovanni Vincentelli | 3.00 | 0/64 |

**MATH UN1207 HONORS MATHEMATICS A.** *4.00 points*.

Prerequisites: (see Courses for First-Year Students). The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)

Fall 2024: MATH UN1207 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 1207 | 001/11865 | T Th 1:10pm - 2:25pm 140 Uris Hall |
Giulia Sacca | 4.00 | 47/52 |

**MATH UN1208 HONORS MATHEMATICS B.** *4.00 points*.

Prerequisites: (see Courses for First-Year Students).

Prerequisites: (see Courses for First-Year Students). The second term of this course may not be taken without the first. Multivariable calculus and linear algebra from a rigorous point of view. Recommended for mathematics majors. Fulfills the linear algebra requirement for the major. (SC)

Spring 2025: MATH UN1208 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 1208 | 001/15314 | T Th 1:10pm - 2:25pm Room TBA |
Jeanne Boursier | 4.00 | 0/64 |

**MATH UN2000 INTRO TO HIGHER MATHEMATICS.** *3.00 points*.

Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA)

Fall 2024: MATH UN2000 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 2000 | 001/00013 | M W 10:10am - 11:25am 328 Milbank Hall |
Dusa McDuff | 3.00 | 28/55 |

Spring 2025: MATH UN2000 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2000 | 001/15319 | T Th 1:10pm - 2:25pm Room TBA |
Giulia Sacca | 3.00 | 0/49 |

**MATH BC2001 PERSPECTIVES IN MATHEMATICS.** *1.00 point*.

Prerequisites: some calculus or the instructor's permission. Intended as an enrichment to the mathematics curriculum of the first years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics

**MATH BC2006 COMBINATORICS.** *3.00 points*.

**MATH UN2010 LINEAR ALGEBRA.** *3.00 points*.

Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)

Fall 2024: MATH UN2010 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2010 | 001/00014 | M W 10:10am - 11:25am Ll002 Milstein Center |
Cristian Iovanov | 3.00 | 82/90 |

MATH 2010 | 002/00015 | M W 11:40am - 12:55pm 405 Milbank Hall |
Cristian Iovanov | 3.00 | 98/110 |

MATH 2010 | 003/11867 | M W 2:40pm - 3:55pm 142 Uris Hall |
Siddhi Krishna | 3.00 | 40/100 |

MATH 2010 | 004/11868 | T Th 10:10am - 11:25am 312 Mathematics Building |
Amadou Bah | 3.00 | 80/100 |

MATH 2010 | 005/11869 | T Th 1:10pm - 2:25pm 203 Mathematics Building |
Amadou Bah | 3.00 | 78/100 |

Spring 2025: MATH UN2010 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2010 | 001/00487 | M W 8:40am - 9:55am 263 Macy Hall |
0. FACULTY | 3.00 | 0/100 |

MATH 2010 | 002/00491 | M W 2:40pm - 3:55pm Ll002 Milstein Center |
Lindsay Piechnik | 3.00 | 0/90 |

MATH 2010 | 003/15325 | T Th 10:10am - 11:25am Room TBA |
Qiao He | 3.00 | 0/100 |

MATH 2010 | 004/15328 | T Th 11:40am - 12:55pm Room TBA |
Qiao He | 3.00 | 0/100 |

MATH 2010 | 005/15331 | T Th 4:10pm - 5:25pm Room TBA |
Elliott Stein | 3.00 | 0/64 |

**MATH UN2020 Honors Linear Algebra.** *3 points*.

**Not offered during 2023-2024 academic year.**

*Prerequisites: MATH UN1201. * A more extensive treatment of the material in MATH UN2010, with increased emphasis on proof. Not to be taken in addition to MATH UN2010 or MATH UN1207-MATH UN1208.

**MATH UN2030 ORDINARY DIFFERENTIAL EQUATIONS.** *3.00 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent. Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications

Fall 2024: MATH UN2030 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 2030 | 001/11872 | M W 1:10pm - 2:25pm 312 Mathematics Building |
Panagiota Daskalopoulos | 3.00 | 88/100 |

MATH 2030 | 002/11873 | T Th 10:10am - 11:25am 142 Uris Hall |
Jeanne Boursier | 3.00 | 49/100 |

MATH 2030 | 003/11874 | T Th 1:10pm - 2:25pm 520 Mathematics Building |
Jeanne Boursier | 3.00 | 30/49 |

Spring 2025: MATH UN2030 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2030 | 001/15344 | M W 10:10am - 11:25am Room TBA |
Dawei Shen | 3.00 | 0/100 |

MATH 2030 | 002/15345 | T Th 11:40am - 12:55pm Room TBA |
Panagiota Daskalopoulos | 3.00 | 0/100 |

**MATH UN2500 ANALYSIS AND OPTIMIZATION.** *3.00 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent and MATH UN2010. Mathematical methods for economics. Quadratic forms, Hessian, implicit functions. Convex sets, convex functions. Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus of variations and optimal control. (SC)

Fall 2024: MATH UN2500 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 2500 | 001/11875 | M W 4:10pm - 5:25pm 417 Mathematics Building |
Qiao He | 3.00 | 49/64 |

MATH 2500 | 002/11876 | T Th 10:10am - 11:25am 517 Hamilton Hall |
Roger Van Peski | 3.00 | 50/75 |

Spring 2025: MATH UN2500 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 2500 | 001/15346 | T Th 10:10am - 11:25am Room TBA |
Xi Shen | 3.00 | 0/100 |

**MATH UN3007 COMPLEX VARIABLES.** *3.00 points*.

Prerequisites: MATH UN1202 An elementary course in functions of a complex variable.

Prerequisites: MATH UN1202 An elementary course in functions of a complex variable. Fundamental properties of the complex numbers, differentiability, Cauchy-Riemann equations. Cauchy integral theorem. Taylor and Laurent series, poles, and essential singularities. Residue theorem and conformal mapping.(SC)

Fall 2024: MATH UN3007 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3007 | 001/11877 | T Th 11:40am - 12:55pm 312 Mathematics Building |
Ovidiu Savin | 3.00 | 56/100 |

**MATH UN3020 NUMBER THEORY AND CRYPTOGRAPHY.** *3.00 points*.

Prerequisites: one year of calculus.

Prerequisites: one year of calculus. Prerequisite: One year of Calculus. Congruences. Primitive roots. Quadratic residues. Contemporary applications

Spring 2025: MATH UN3020 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3020 | 001/15349 | M W 10:10am - 11:25am Room TBA |
Siddhi Krishna | 3.00 | 0/100 |

**MATH UN3025 MAKING, BREAKING CODES.** *3.00 points*.

Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and and MATH UN2010.

Prerequisites: (MATH UN1101 and MATH UN1102 and MATH UN1201) and and MATH UN2010. A concrete introduction to abstract algebra. Topics in abstract algebra used in cryptography and coding theory

Fall 2024: MATH UN3025 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3025 | 001/11878 | T Th 1:10pm - 2:25pm 312 Mathematics Building |
Dorian Goldfeld | 3.00 | 96/100 |

**MATH UN3027 Ordinary Differential Equations.** *3 points*.

Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.

Corequisites: MATH UN2010

Equations of order one; systems of linear equations. Second-order equations. Series solutions at regular and singular points. Boundary value problems. Selected applications.

**MATH UN3028 PARTIAL DIFFERENTIAL EQUATIONS.** *3.00 points*.

Prerequisites: MATH UN3027 and MATH UN2010 or the equivalent

Prerequisites: (MATH UN2010 and MATH UN2030) or the equivalent introduction to partial differential equations. First-order equations. Linear second-order equations; separation of variables, solution by series expansions. Boundary value problems

Spring 2025: MATH UN3028 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
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MATH 3028 | 001/15351 | T Th 1:10pm - 2:25pm Room TBA |
Simon Brendle | 3.00 | 0/64 |

**MATH UN3050 DISCRETE TIME MODELS IN FINANC.** *3.00 points*.

Prerequisites: (MATH UN1102 and MATH UN1201) or (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH UN2010 Recommended: MATH UN3027 (or MATH UN2030 and SIEO W3600).

Prerequisites: (MATH UN1102 and MATH UN1201) or (MATH UN1101 and MATH UN1102 and MATH UN1201) and MATH UN2010 Recommended: MATH UN3027 (or MATH UN2030 and SIEO W3600). Elementary discrete time methods for pricing financial instruments, such as options. Notions of arbitrage, risk-neutral valuation, hedging, term-structure of interest rates

Spring 2025: MATH UN3050 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3050 | 001/15353 | M W 6:10pm - 7:25pm Room TBA |
Mikhail Smirnov | 3.00 | 0/64 |

**MATH UN3386 DIFFERENTIAL GEOMETRY.** *3.00 points*.

Prerequisites: MATH UN1202 or the equivalent.

Local and global differential geometry of submanifolds of Euclidiean 3-space. Frenet formulas for curves. Various types of curvatures for curves and surfaces and their relations. The Gauss-Bonnet theorem.

**MATH UN3901 SUPERVISED READINGS I.** *1.00-3.00 points*.

Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the Director of Undergraduate Studies. The written permission must be deposited with the Director of Undergraduate Studies before registration is completed. Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor. Supervising Readings do NOT count towards major requirements, with the exception of an advanced written approval by the DUS

Fall 2024: MATH UN3901 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3901 | 001/00790 | |
Dusa McDuff | 1.00-3.00 | 1/5 |

MATH 3901 | 002/00791 | |
Daniela De Silva | 1.00-3.00 | 0/5 |

MATH 3901 | 003/17561 | |
Richard Hamilton | 1.00-3.00 | 1/1 |

MATH 3901 | 004/19472 | |
Elena Giorgi | 1.00-3.00 | 2/2 |

MATH 3901 | 005/20931 | |
Peter Woit | 1.00-3.00 | 1/1 |

MATH 3901 | 006/21153 | |
Chiu-Chu Liu | 1.00-3.00 | 1/1 |

MATH 3901 | 007/21214 | |
Robert Friedman | 1.00-3.00 | 1/1 |

MATH 3901 | 008/21255 | |
Dorian Goldfeld | 1.00-3.00 | 1/1 |

**MATH UN3902 SUPERVISED READINGS II.** *1.00-3.00 points*.

Prerequisites: The written permission of the faculty member who agrees to act as sponsor (sponsorship limited to full-time instructors on the staff list), as well as the permission of the Director of Undergraduate Studies. The written permission must be deposited with the Director of Undergraduate Studies before registration is completed. Guided reading and study in mathematics. A student who wishes to undertake individual study under this program must present a specific project to a member of the staff and secure his or her willingness to act as sponsor. Written reports and periodic conferences with the instructor. Supervising Readings do NOT count towards major requirements, with the exception of an advanced written approval by the DUS

**MATH UN3951 UNDERGRADUATE SEMINARS I.** *3.00 points*.

Prerequisites: Two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

Prerequisites: Two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies permission. The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow

Fall 2024: MATH UN3951 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3951 | 001/00078 | |
Cristian Iovanov | 3.00 | 50/64 |

**MATH UN3952 UNDERGRADUATE SEMINARS II.** *3.00 points*.

Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission.

Prerequisites: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission. The subject matter is announced at the start of registration and is different in each section. Each student prepares talks to be given to the seminar, under the supervision of a faculty member or senior teaching fellow. Prerequisite: two years of calculus, at least one year of additional mathematics courses, and the director of undergraduate studies' permission

Spring 2025: MATH UN3952 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3952 | 001/00804 | |
Alisa Knizel | 3.00 | 0/80 |

**MATH UN3997 SUPERVISED INDIVIDUAL RESEARCH.** *1.00-4.00 points*.

Prerequisites: the written permission of the faculty member who agrees to act as a supervisor, and the director of undergraduate studies permission. For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member

Fall 2024: MATH UN3997 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 3997 | 001/00079 | |
Dusa McDuff | 1.00-4.00 | 1/5 |

**MATH UN3998 SUPERVISED INDIVIDUAL RESEARCH.** *3.00 points*.

*Prerequisites: The written permission of the faculty member who agrees to act as a supervisor, and the permission of the Director of Undergraduate Studies.* For specially selected mathematics majors, the opportunity to write a senior thesis on a problem in contemporary mathematics under the supervision of a faculty member.

**MATH GU4007 ANALYTIC NUMBER THEORY.** *3.00 points*.

Prerequisites: MATH UN3007

Prerequisites: MATH UN3007 A one semeser course covering the theory of modular forms, zeta functions, L -functions, and the Riemann hypothesis. Particular topics covered include the Riemann zeta function, the prime number theorem, Dirichlet characters, Dirichlet L-functions, Siegel zeros, prime number theorem for arithmetic progressions, SL (2, Z) and subgroups, quotients of the upper half-plane and cusps, modular forms, Fourier expansions of modular forms, Hecke operators, L-functions of modular forms

Spring 2025: MATH GU4007 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4007 | 001/15355 | T Th 2:40pm - 3:55pm Room TBA |
Amadou Bah | 3.00 | 0/20 |

**MATH GU4032 FOURIER ANALYSIS.** *3.00 points*.

Prerequisites: three terms of calculus and linear algebra or four terms of calculus.

Prerequisites: three terms of calculus and linear algebra or four terms of calculus. Prerequisite: three terms of calculus and linear algebra or four terms of calculus. Fourier series and integrals, discrete analogues, inversion and Poisson summation formulae, convolution. Heisenberg uncertainty principle. Stress on the application of Fourier analysis to a wide range of disciplines

Fall 2024: MATH GU4032 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4032 | 001/11879 | T Th 10:10am - 11:25am 603 Hamilton Hall |
Simon Brendle | 3.00 | 30/49 |

**MATH GU4041 INTRO MODERN ALGEBRA I.** *3.00 points*.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Groups, homomorphisms, normal subgroups, the isomorphism theorems, symmetric groups, group actions, the Sylow theorems, finitely generated abelian groups

Fall 2024: MATH GU4041 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4041 | 001/11904 | M W 1:10pm - 2:25pm 203 Mathematics Building |
Robert Friedman | 3.00 | 68/110 |

Spring 2025: MATH GU4041 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 4041 | 001/15358 | M W 2:40pm - 3:55pm Room TBA |
Michael Thaddeus | 3.00 | 0/64 |

**MATH GU4042 INTRO MODERN ALGEBRA II.** *3.00 points*.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent.

Prerequisites: MATH UN1102 and MATH UN1202 and MATH UN2010 or the equivalent. The second term of this course may not be taken without the first. Rings, homomorphisms, ideals, integral and Euclidean domains, the division algorithm, principal ideal and unique factorization domains, fields, algebraic and transcendental extensions, splitting fields, finite fields, Galois theory

Fall 2024: MATH GU4042 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4042 | 001/11846 | M W 10:10am - 11:25am 417 Mathematics Building |
Michael Thaddeus | 3.00 | 17/49 |

Spring 2025: MATH GU4042 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 4042 | 001/15360 | M W 2:40pm - 3:55pm Room TBA |
Robert Friedman | 3.00 | 0/49 |

**MATH GU4043 ALGEBRAIC NUMBER THEORY.** *3.00 points*.

Prerequisites: MATH GU4041 and MATH GU4042 or the equivalent

Prerequisites: MATH GU4041 and MATH GU4042 or the equivalent Algebraic number fields, unique factorization of ideals in the ring of algebraic integers in the field into prime ideals. Dirichlet unit theorem, finiteness of the class number, ramification. If time permits, p-adic numbers and Dedekind zeta function

Spring 2025: MATH GU4043 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4043 | 001/15362 | T Th 4:10pm - 5:25pm Room TBA |
Yujie Xu | 3.00 | 0/20 |

**MATH GU4044 REPRESENTATNS OF FINITE GROUPS.** *3.00 points*.

Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent.

Prerequisites: MATH UN2010 and MATH GU4041 or the equivalent. Finite groups acting on finite sets and finite dimensional vector spaces. Group characters. Relations with subgroups and factor groups. Arithmetic properties of character values. Applications to the theory of finite groups: Frobenius groups, Hall subgroups and solvable groups. Characters of the symmetric groups. Spherical functions on finite groups

Fall 2024: MATH GU4044 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4044 | 001/11880 | T Th 1:10pm - 2:25pm 407 Mathematics Building |
Andrei Okounkov | 3.00 | 15/30 |

**MATH GU4045 ALGEBRAIC CURVES.** *3.00 points*.

Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007

Prerequisites: (MATH GU4041 and MATH GU4042) and MATH UN3007 Plane curves, affine and projective varieties, singularities, normalization, Riemann surfaces, divisors, linear systems, Riemann-Roch theorem

Spring 2025: MATH GU4045 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4045 | 001/15365 | M W 11:40am - 12:55pm Room TBA |
Yoonjoo Kim | 3.00 | 0/20 |

**MATH W4046 Introduction to Category Theory.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement**Not offered during 2023-2024 academic year.**

Prerequisites: *MATH W4041*.

Categories, functors, natural transformations, adjoint functors, limits and colimits, introduction to higher categories and diagrammatic methods in algebra.

**MATH GU4051 TOPOLOGY.** *3.00 points*.

Prerequisites: (MATH UN1202 and MATH UN2010) and rudiments of group theory (e.g., MATH GU4041). MATH UN1208 or MATH GU4061 is recommended, but not required.

Prerequisites: (MATH UN1202 and MATH UN2010) and rudiments of group theory (e.g. MATH GU4041). MATH UN1208 or MATH GU4061 is recommended, but not required. Metric spaces, continuity, compactness, quotient spaces. The fundamental group of topological space. Examples from knot theory and surfaces. Covering spaces

Fall 2024: MATH GU4051 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4051 | 001/11881 | T Th 6:10pm - 7:25pm 520 Mathematics Building |
Rostislav Akhmechet | 3.00 | 18/49 |

**MATH GU4052 INTRODUCTION TO KNOT THEORY.** *3.00 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: MATH GU4051 Topology and / or MATH GU4061 Introduction To Modern Analysis I (or equivalents). Recommended (can be taken concurrently): MATH UN2010 linear algebra, or equivalent.

Prerequisites: MATH GU4051 Topology and / or MATH GU4061 Introduction To Modern Analysis I (or equivalents). Recommended (can be taken concurrently): MATH UN2010 linear algebra, or equivalent. The study of algebraic and geometric properties of knots in R＾3, including but not limited to knot projections and Reidemeisters theorm, Seifert surfaces, braids, tangles, knot polynomials, fundamental group of knot complements. Depending on time and student interest, we will discuss more advanced topics like knot concordance, relationship to 3-manifold topology, other algebraic knot invariants

Fall 2024: MATH GU4052 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4052 | 001/11882 | M W 11:40am - 12:55pm 307 Mathematics Building |
Siddhi Krishna | 3.00 | 10/20 |

**MATH GU4053 INTRO TO ALGEBRAIC TOPOLOGY.** *3.00 points*.

Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051

Prerequisites: MATH UN2010 and MATH GU4041 and MATH GU4051 The study of topological spaces from algebraic properties, including the essentials of homology and the fundamental group. The Brouwer fixed point theorem. The homology of surfaces. Covering spaces

Spring 2025: MATH GU4053 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4053 | 001/15367 | T Th 11:40am - 12:55pm Room TBA |
0. FACULTY | 3.00 | 0/20 |

**MATH GU4061 INTRO MODERN ANALYSIS I.** *3.00 points*.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, Ascoli-Arzela theorem, Stone-Weierstrass theorem

Fall 2024: MATH GU4061 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4061 | 001/11858 | T Th 1:10pm - 2:25pm 417 Mathematics Building |
Sven Hirsch | 3.00 | 54/64 |

MATH 4061 | 002/11859 | T Th 2:40pm - 3:55pm 417 Mathematics Building |
3.00 | 63/64 | |

Spring 2025: MATH GU4061 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 4061 | 001/15369 | M W 1:10pm - 2:25pm Room TBA |
Julien Dubedat | 3.00 | 0/100 |

**MATH GU4062 INTRO MODERN ANALYSIS II.** *3.00 points*.

Prerequisites: MATH UN1202 or the equivalent, and MATH UN2010. The second term of this course may not be taken without the first.

The second term of this course may not be taken without the first. Power series, analytic functions, Implicit function theorem, Fubini theorem, change of variables formula, Lebesgue measure and integration, function spaces

Fall 2024: MATH GU4062 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4062 | 001/11883 | M W 11:40am - 12:55pm 520 Mathematics Building |
Milind Hegde | 3.00 | 12/49 |

Spring 2025: MATH GU4062 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

MATH 4062 | 001/15370 | T Th 4:10pm - 5:25pm Room TBA |
Francesco Lin | 3.00 | 0/49 |

**MATH GU4065 HONORS COMPLEX VARIABLES.** *3.00 points*.

Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061

Prerequisites: (MATH UN1207 and MATH UN1208) or MATH GU4061 A theoretical introduction to analytic functions. Holomorphic functions, harmonic functions, power series, Cauchy-Riemann equations, Cauchy's integral formula, poles, Laurent series, residue theorem. Other topics as time permits: elliptic functions, the gamma and zeta function, the Riemann mapping theorem, Riemann surfaces, Nevanlinna theory

Fall 2024: MATH GU4065 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4065 | 001/11884 | T Th 11:40am - 12:55pm 520 Mathematics Building |
Francesco Lin | 3.00 | 35/45 |

**MATH GU4071 Introduction to the Mathematics of Finance.** *3 points*.

CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: MATH UN1202 and MATH UN3027 and STAT W4150 and SEIO W4150, or their equivalents.

The mathematics of finance, principally the problem of pricing of derivative securities, developed using only calculus and basic probability. Topics include mathematical models for financial instruments, Brownian motion, normal and lognormal distributions, the BlackûScholes formula, and binomial models.

**MATH GU4081 INTRO-DIFFERENTIABLE MANIFOLDS.** *3.00 points*.

Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010

Prerequisites: (MATH GU4051 or MATH GU4061) and MATH UN2010 Concept of a differentiable manifold. Tangent spaces and vector fields. The inverse function theorem. Transversality and Sards theorem. Intersection theory. Orientations. Poincare-Hopf theorem. Differential forms and Stokes theorem

Spring 2025: MATH GU4081 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4081 | 001/15373 | M W 10:10am - 11:25am Room TBA |
Sven Hirsch | 3.00 | 0/49 |

**MATH GU4155 PROBABILITY THEORY.** *3.00 points*.

Prerequisites: MATH GU4061 or MATH UN3007

Prerequisites: MATH GU4061 or MATH UN3007 A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. Generating functions. Convergence in probability and in distribution. Discrete probability spaces, recurrence and transience of random walks. Infinite models, proof of the law of large numbers and the central limit theorem. Markov chains

Fall 2024: MATH GU4155 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

MATH 4155 | 001/11860 | T Th 2:40pm - 3:55pm 507 Mathematics Building |
Ivan Corwin | 3.00 | 14/26 |

**MATH GU4392 INTRO TO QUANTUM MECHANICS II.** *3.00 points*.

Continuation of GU4391. This course will focus on quantum mechanics, paying attention to both the underlying mathematical structures as well as their physical motivations and consequences. It is meant to be accessible to students with no previous formal training in quantum theory. The role of symmetry, groups and representations will be stressed.

**SIEO W3600 INTRO PROBABILITY/STATISTICS.** *4.00 points*.

**SIEO W4150 INTRO-PROBABILITY ＆ STATISTICS.** *3.00 points*.

## Cross-Listed Courses

### Computer Science

**COMS S3251 Computational Linear Algebra.** *3 points*.

**Not offered during 2023-2024 academic year.**

Prerequisites: two terms of calculus.

Computational linear algebra, solution of linear systems, sparse linear systems, least squares, eigenvalue problems, and numerical solution of other multivariate problems as time permits.

**COMS W4203 Graph Theory.** *3 points*.

Lect: 3.

Prerequisites: (COMS W3203)

General introduction to graph theory. Isomorphism testing, algebraic specification, symmetries, spanning trees, traversability, planarity, drawings on higher-order surfaces, colorings, extremal graphs, random graphs, graphical measurement, directed graphs, Burnside-Polya counting, voltage graph theory.

**COMS W3203 DISCRETE MATHEMATICS.** *4.00 points*.

Lect: 3.

Prerequisites: Any introductory course in computer programming.

Logic and formal proofs, sequences and summation, mathematical induction, binomial coefficients, elements of finite probability, recurrence relations, equivalence relations and partial orderings, and topics in graph theory (including isomorphism, traversability, planarity, and colorings)

Fall 2024: COMS W3203 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

COMS 3203 | 001/11935 | M W 4:10pm - 5:25pm 301 Pupin Laboratories |
Tony Dear | 4.00 | 198/270 |

Spring 2025: COMS W3203 |
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Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |

COMS 3203 | 001/13386 | M W 2:40pm - 3:55pm Room TBA |
Tony Dear | 4.00 | 0/164 |

### Industrial Engineering and Operations Research

**CSOR E4010 GRAPH THEORY: COMBINATL VIEW.** *3.00 points*.

Lect: 3.**Not offered during 2023-2024 academic year.**

Prerequisites: Linear Algebra, or instructor's permission.

An introductory course in graph theory with emphasis on its combinatorial aspects. Basic definitions, and some fundamental topics in graph theory and its applications. Topics include trees and forests graph coloring, connectivity, matching theory and others