# Courses

- AS.110.105 - Introduction to Calculus
This course starts from scratch and provides students with all the background necessary for the study of calculus. It includes a review of algebra, trigonometry, exponential and logarithmic functions, coordinates and graphs. Each of these tools will be introduced in its cultural and historical context. The concept of the rate of change of a function will be introduced. Not open to students who have studied calculus in high school.

**Credits:**4.00**Instructor:**Clingman, Tslil**Term:**Fall 2017**Meetings:**MWF 9:00AM - 9:50AM, T 1:30PM - 2:20PM**Status:**Open - AS.110.107 - Calculus II (For Biological and Social Science)
Differential and integral Calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions. Applications to the biological and social sciences will be discussed, and the courses are designed to meet the needs of students in these disciplines.

**Credits:**4.00**Instructor:**Zheng, Xudong**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 4:30PM - 5:20PM**Status:**Open - AS.110.108 - Calculus I
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, and the courses are designed to meet the needs of students in these disciplines.

**Credits:**4.00**Instructor:**Sun, Liming**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 1:30PM - 2:20PM**Status:**Open - AS.110.109 - Calculus II (For Physical Sciences and Engineering)
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, and the courses are designed to meet the needs of students in these disciplines.

**Credits:**4.00**Instructor:**Wang, Yi**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 1:30PM - 2:20PM**Status:**Waitlist Only - AS.110.107 - Calculus II (For Biological and Social Science)
Differential and integral Calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions. Applications to the biological and social sciences will be discussed, and the courses are designed to meet the needs of students in these disciplines.

**Credits:**4.00**Instructor:**Zheng, Xudong**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 3:00PM - 3:50PM**Status:**Open - AS.110.113 - Honors One Variable Calculus
This is an honors alternative to the Calculus sequences AS.110.106-AS.110.107 or AS.110.108-AS.110.109 and meets the general requirement for both Calculus I and Calculus II (although the credit hours count for only one course). It is a more theoretical treatment of one variable differential and integral calculus and is based on our modern understanding of the real number system as explained by Cantor, Dedekind, and Weierstrass. Students who want to know the "why's and how's" of Calculus will find this course rewarding. Previous background in Calculus is not assumed. Students will learn differential Calculus (derivatives, differentiation, chain rule, optimization, related rates, etc), the theory of integration, the fundamental theorem(s) of Calculus, applications of integration, and Taylor series. Students should have a strong ability to learn mathematics quickly and on a higher level than that of the regular Calculus sequences.

**Credits:**4.00**Instructor:**Nakade, Apurva**Term:**Fall 2017**Meetings:**MW 1:30PM - 2:45PM, F 1:30PM - 2:20PM**Status:**Open - AS.110.106 - Calculus I (Biology and Social Sciences)
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions. Many applications to the biological and social sciences will be discussed.

**Credits:**4.00**Instructor:**Brown, Richard**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 3:00PM - 3:50PM**Status:**Waitlist Only - AS.110.108 - Calculus I
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor's theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, and the courses are designed to meet the needs of students in these disciplines.

**Credits:**4.00**Instructor:**Sun, Liming**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 3:00PM - 3:50PM**Status:**Open - AS.110.106 - Calculus I (Biology and Social Sciences)
Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, introduction to differential equations, functions of several variables, linear systems, applications for systems of linear differential equations, probability distributions. Many applications to the biological and social sciences will be discussed.

**Credits:**4.00**Instructor:**Brown, Richard**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 4:30PM - 5:20PM**Status:**Open - AS.110.109 - Calculus II (For Physical Sciences and Engineering)
**Credits:**4.00**Instructor:**Wang, Yi**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 3:00PM - 3:50PM**Status:**Open - AS.110.201 - Linear Algebra
Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations.

**Credits:**4.00**Instructor:**Specter, Joel Benjamin**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 3:00PM - 3:50PM**Status:**Open - AS.110.201 - Linear Algebra
Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations.

**Credits:**4.00**Instructor:**Specter, Joel Benjamin**Term:**Fall 2017**Meetings:**MWF 10:00AM - 10:50AM, T 1:30PM - 2:20PM**Status:**Open - AS.110.202 - Calculus III
Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem.

**Credits:**4.00**Instructor:**Murphy, James**Term:**Fall 2017**Meetings:**MWF 11:00AM - 11:50AM, T 1:30PM - 2:20PM**Status:**Waitlist Only - AS.110.202 - Calculus III
Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem.

**Credits:**4.00**Instructor:**Murphy, James**Term:**Fall 2017**Meetings:**MWF 11:00AM - 11:50AM, T 4:30PM - 5:20PM**Status:**Open - AS.110.212 - Honors Linear Algebra
This course includes the material in AS.110.201 with some additional applications and theory. Recommended for mathematically able students majoring in physical science, engineering, or mathematics. AS.110.211-AS.110.212 used to be an integrated yearlong course, but now the two are independent courses and can be taken in either order. This course satisfies a requirement for the math major that the nonhonors version does not.

**Credits:**4.00**Instructor:**Vigogna, Stefano**Term:**Fall 2017**Meetings:**MW 1:30PM - 2:45PM, F 1:30PM - 2:20PM**Status:**Open - AS.110.202 - Calculus III
Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem.

**Credits:**4.00**Instructor:**Murphy, James**Term:**Fall 2017**Meetings:**MWF 12:00PM - 12:50PM, T 3:00PM - 3:50PM**Status:**Waitlist Only - AS.110.401 - Advanced Algebra I
This is an introduction to group theory, with an emphasis on concrete examples, and especially on geometric symmetry groups. The course will introduce basic notions (groups, subgroups, homomorphisms, quotients) and prove foundational results (Lagrange's theorem, Cauchy's theorem, orbit-counting techniques, the classification of finite abelian groups). Examples to be discussed include permutation groups, dihedral groups, matrix groups, and finite rotation groups, culminating in the classification of the wallpaper groups. This is also an Introduction to Proofs course (IP) and may be taken as a first proof-based mathematics course. This course satisfies a core requirement of the mathematics major. Course Prerequisite: 110.201 Linear Algebra or equivalent.

**Credits:**4.00**Instructor:**Savitt, David Lawrence**Term:**Fall 2017**Meetings:**MW 12:00PM - 1:15PM, F 12:00PM - 12:50PM**Status:**Open - AS.110.321 - Honors Complex Analysis
This course is an introduction to the theory of functions of one complex variable for honors students. Its emphasis is on techniques and applications, and it serves as a basis for more advanced courses. Topics will include functions of a complex variable and their derivatives; power series and Laurent expansions; Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions, as well as applications to number theory and harmonic analysis.

**Credits:**4.00**Instructor:**Staff**Term:**Fall 2017**Meetings:**TTh 12:00PM - 1:15PM**Status:**Canceled - AS.110.415 - Honors Analysis I
This highly theoretical sequence in analysis is reserved for the most able students. The sequence covers the real number system, metric spaces, basic functional analysis, the Lebesgue integral, and other topics.

**Credits:**4.00**Instructor:**Sogge, Christopher**Term:**Fall 2017**Meetings:**MW 1:30PM - 2:45PM, F 1:30PM - 2:20PM**Status:**Open - AS.110.302 - Differential Equations and Applications
This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. The purpose of the course is to familiarize the student with the techniques of solving ordinary differential equations. The specific subjects to be covered include first order differential equations, second order linear differential equations, applications to electric circuits, oscillation of solutions, power series solutions, systems of linear differential equations, autonomous systems, Laplace transforms and linear differential equations, mathematical models (e.g., in the sciences or economics).

**Credits:**4.00**Instructor:**Luehrmann, Jonas**Term:**Fall 2017**Meetings:**MWF 12:00PM - 12:50PM, T 1:30PM - 2:20PM**Status:**Waitlist Only - AS.110.443 - Fourier Analysis
An introduction to the Fourier transform and the construction of fundamental solutions of linear partial differential equations. Homogeneous distributions on the real line: the Dirac delta function, the Heaviside step function. Operations with distributions: convolution, differentiation, Fourier transform. Construction of fundamental solutions of the wave, heat, Laplace and Schrödinger equations. Singularities of fundamental solutions and their physical interpretations (e.g., wave fronts). Fourier analysis of singularities, oscillatory integrals, method of stationary phase.

**Credits:**4.00**Instructor:**Tang, Sui**Term:**Fall 2017**Meetings:**TTh 10:30AM - 11:45AM**Status:**Open - AS.110.405 - Analysis I
This course is designed to give a firm grounding in the basic tools of analysis. It is recommended as preparation (but may not be a prerequisite) for other advanced analysis courses. Real and complex number systems, topology of metric spaces, limits, continuity, infinite sequences and series, differentiation, Riemann-Stieltjes integration.

**Credits:**4.00**Instructor:**Xu, Hang**Term:**Fall 2017**Meetings:**MW 1:30PM - 2:45PM, F 1:30PM - 2:20PM**Status:**Open - AS.110.411 - Honors Algebra I
An introduction to the basic notions of modern algebra for students with some prior acquaintance with abstract mathematics. Elements of group theory: groups, subgroups, normal subgroups, quotients, homomorphisms. Generators and relations, free groups, products, abelian groups, finite groups. Groups acting on sets, the Sylow theorems. Definition and examples of rings and ideals.

**Credits:**4.00**Instructor:**Riehl, Emily**Term:**Fall 2017**Meetings:**MW 12:00PM - 1:15PM, F 12:00PM - 12:50PM**Status:**Closed - AS.110.441 - Calculus on Manifolds
This course provides the tools for classical three-dimensional physics and mechanics. This course extends these techniques to the general locally Euclidean spaces (manifolds) needed for an understanding of such things as Maxwell's equations or optimization in higher dimensional contexts, eg. in economics. The course will cover the theory of differential forms and integration. Specific topics include Maxwell's equations in terms of 4D Lorentz geometry, vector (in particular, tangent) bundles, an introduction to de Rham theory, and Sard's theorem on the density of regular values of smooth functions. The course is intended to be useful to mathematics students interested in analysis, differential geometry, and topology, as well as to students in physics and economics.

**Credits:**4.00**Instructor:**Morava, Jack**Term:**Fall 2017**Meetings:**TTh 3:00PM - 4:15PM**Status:**Open - AS.110.202 - Calculus III
**Credits:**4.00**Instructor:**Murphy, James**Term:**Fall 2017**Meetings:**MWF 11:00AM - 11:50AM, T 3:00PM - 3:50PM**Status:**Open - AS.110.311 - Methods of Complex Analysis
This course is an introduction to the theory of functions of one complex variable. Its emphasis is on techniques and applications, and it serves as a basis for more advanced courses. Functions of a complex variable and their derivatives; power series and Laurent expansions; Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions.

**Credits:**4.00**Instructor:**Xu, Hang**Term:**Fall 2017**Meetings:**TTh 12:00PM - 1:15PM**Status:**Open - AS.110.407 - Honors Complex Analysis
AS.110.407. Honors Complex Analysis. 4.00 Credits. This course is an introduction to the theory of functions of one complex variable for honors students. Its emphasis is on techniques and applications, and can serve as an Introduction to Proofs (IP) course. Topics will include functions of a complex variable and their derivatives; power series and Laurent expansions; Cauchy integral theorem and formula; calculus of residues and contour integrals; harmonic functions, as well as applications to number theory and harmonic analysis. Area: Quantitative and Mathematical Sciences.

**Credits:**4.00**Instructor:**Bernstein, Jacob**Term:**Fall 2017**Meetings:**TTh 12:00PM - 1:15PM**Status:**Open - AS.110.439 - Introduction To Differential Geometry
Theory of curves and surfaces in Euclidean space: Frenet equations, fundamental forms, curvatures of a surface, theorems of Gauss and Mainardi-Codazzi, curves on a surface; introduction to tensor analysis and Riemannian geometry; theorema egregium; elementary global theorems.

**Credits:**4.00**Instructor:**Morava, Jack**Term:**Fall 2017**Meetings:**TTh 1:30PM - 2:45PM**Status:**Waitlist Only - AS.110.304 - Elementary Number Theory
The student is provided with many historical examples of topics, each of which serves as an illustration of and provides a background for many years of current research in number theory. Primes and prime factorization, congruences, Euler's function, quadratic reciprocity, primitive roots, solutions to polynomial congruences (Chevalley's theorem), Diophantine equations including the Pythagorean and Pell equations, Gaussian integers, Dirichlet's theorem on primes.

**Credits:**4.00**Instructor:**Kong, Jian**Term:**Fall 2017**Meetings:**TTh 9:00AM - 10:15AM**Status:**Open - AS.110.225 - Problem Solving Lab
This course is an introduction to mathematical reason and formalism in the context of mathematical problem solving, such as induction, invariants, inequalities and generating functions. This course does not satisfy any major requirement, and may be taken more than once for credit It is primarily used as training for the William Lowell Putnam Mathematics Competition. Area: Quantitative and Mathematical Sciences.

**Credits:**2.00**Instructor:**Savitt, David Lawrence**Term:**Fall 2017**Meetings:**Th 4:00PM - 5:40PM**Status:**Open - AS.110.302 - Differential Equations and Applications
This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. The purpose of the course is to familiarize the student with the techniques of solving ordinary differential equations. The specific subjects to be covered include first order differential equations, second order linear differential equations, applications to electric circuits, oscillation of solutions, power series solutions, systems of linear differential equations, autonomous systems, Laplace transforms and linear differential equations, mathematical models (e.g., in the sciences or economics).

**Credits:**4.00**Instructor:**Luehrmann, Jonas**Term:**Fall 2017**Meetings:**MWF 12:00PM - 12:50PM, T 3:00PM - 3:50PM**Status:**Open