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MATH 20: Algebra and Multivariable Mathematics for Social Sciences
4.00 Credits
Harvard University
Introduction to linear algebra, including vectors, matrices, and applications. Calculus of functions of several variables, including partial derivatives, constrained and unconstrained optimization, and applications. Covers the topics from Mathematics 21a,b which are most important in applications to economics, the social sciences, and some other fields.
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MATH 20 - Algebra and Multivariable Mathematics for Social Sciences
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MATH 21a: Multivariable Calculus
4.00 Credits
Harvard University
To see how calculus applies in practical situations described by more than one variable, we study: Vectors, lines, planes, parameterization of curves and surfaces, partial derivatives, directional derivatives, and the gradient, optimization and critical point analysis, including constrained optimization and the Method of Lagrange Multipliers, integration over curves, surfaces, and solid regions using Cartesian, polar, cylindrical, and spherical coordinates, divergence and curl of vector fields, and the Green's, Stokes', and Divergence Theorems.
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MATH 21a - Multivariable Calculus
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MATH 21b: Linear Algebra and Differential Equations
4.00 Credits
Harvard University
Matrices provide the algebraic structure for solving myriad problems across the sciences. We study matrices and related topics such as vectors, Euclidean spaces, linear transformations, determinants, eigenvalues, and eigenvectors. Of applications given, a regular section considers dynamical systems and both ordinary and partial differential equations plus an introduction to Fourier series.
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MATH 21b - Linear Algebra and Differential Equations
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MATH 23a: Linear Algebra and Real Analysis I
4.00 Credits
Harvard University
A rigorous, integrated treatment of linear algebra and multivariable differential calculus, emphasizing topics that are relevant to fields such as physics and economics. Topics: fields, vector spaces and linear transformations, scalar and vector products, elementary topology of Euclidean space, limits, continuity, and differentiation in n dimensions, eigenvectors and eigenvalues, inverse and implicit functions, manifolds, and Lagrange multipliers. Students are expected to master twenty important proofs.
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MATH 23a - Linear Algebra and Real Analysis I
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MATH 23b: Linear Algebra and Real Analysis II
4.00 Credits
Harvard University
A rigorous, integrated treatment of linear algebra and multivariable calculus. Topics: Riemann and Lebesgue integration, determinants, change of variables, volume of manifolds, differential forms, and exterior derivative. Stokes's theorem is presented both in the language of vector analysis (div, grad, and curl) and in the language of differential forms. Students are expected to master twenty important proofs.
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MATH 23b - Linear Algebra and Real Analysis II
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MATH 25a: Honors Linear Algebra and Real Analysis I
4.00 Credits
Harvard University
A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness.
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MATH 25a - Honors Linear Algebra and Real Analysis I
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MATH 25b: Honors Linear Algebra and Real Analysis II
4.00 Credits
Harvard University
A rigorous treatment of basic analysis. Topics include: convergence, continuity, differentiation, the Riemann integral, uniform convergence, the Stone-Weierstrass theorem, Fourier series, differentiation in several variables. Additional topics, including the classical results of vector calculus in two and three dimensions, as time allows.
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MATH 25b - Honors Linear Algebra and Real Analysis II
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MATH 55a: Honors Abstract Algebra
4.00 Credits
Harvard University
A rigorous treatment of abstract algebra including linear algebra and group theory.
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MATH 55a - Honors Abstract Algebra
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MATH 55b: Honors Real and Complex Analysis
4.00 Credits
Harvard University
A rigorous treatment of real and complex analysis.
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MATH 55b - Honors Real and Complex Analysis
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MATH 60r: Reading Course for Senior Honors Candidates
4.00 Credits
Harvard University
Advanced reading in topics not covered in courses.
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MATH 60r - Reading Course for Senior Honors Candidates
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