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31 - 40 of 83 results for: all courses

MATH 53: Ordinary Differential Equations with Linear Algebra

Ordinary differential equations and initial value problems, systems of linear differential equations with constant coefficients, applications of second-order equations to oscillations, matrix exponentials, Laplace transforms, stability of non-linear systems and phase plane analysis, numerical methods. Prerequisite: 51 or equivalents.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

MATH 61CM: Modern Mathematics: Continuous Methods

This is the first part of a theoretical (i.e., proof-based) sequence in multivariable calculus and linear algebra, providing a unified treatment of these topics. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, metric spaces, differentiation in Euclidean space, submanifolds of Euclidean space, inverse and implicit function theorems, and many examples. Part of the linear algebra content is covered jointly with Math 61DM. Students should know 1-variable calculus and have an interest in a theoretical approach to the subject. Prerequisite: score of 5 on the BC-level Advanced Placement calculus exam, or consent of the instructor.
Terms: Aut | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter (ABCD/NP)

MATH 62CM: Modern Mathematics: Continuous Methods

A continuation of themes from Math 61CM, centered around: manifolds, multivariable integration, and the general Stokes' theorem. This includes a treatment of multilinear algebra, further study of submanifolds of Euclidean space and an introduction to general manifolds (with many examples), differential forms and their geometric interpretations, integration of differential forms, Stokes' theorem, and some applications to topology. Prerequisite: Math 61CM.
Terms: Win | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter (ABCD/NP)

MATH 63CM: Modern Mathematics: Continuous Methods

A proof-based course on ordinary differential equations, continuing themes from Math 61CM and Math 62CM. Topics include linear systems of differential equations and necessary tools from linear algebra, stability and asymptotic properties of solutions to linear systems, existence and uniqueness theorems for nonlinear differential equations with some applications to manifolds, behavior of solutions near an equilibrium point, and Sturm-Liouville theory. Prerequisites: Math 61CM and Math 62CM.
Terms: Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter (ABCD/NP)

MATH 104: Applied Matrix Theory

Linear algebra for applications in science and engineering: orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. ( Math 113 offers a more theoretical treatment of linear algebra.) Prerequisites: Math 51 and programming experience on par with CS106nnMath 104 and EE103/CME103 cover complementary topics in applied linear algebra. The focus of Math 104 is on algorithms and concepts; the focus of EE103 is on a few linear algebra concepts, and many applications.
Terms: Aut, Win | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

MATH 106: Functions of a Complex Variable

Complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy integral formula, residues, elementary conformal mappings. ( Math 116 offers a more theoretical treatment.) Prerequisite: 52.
Terms: Spr, Sum | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

MATH 108: Introduction to Combinatorics and Its Applications

Topics: graphs, trees (Cayley's Theorem, application to phylogony), eigenvalues, basic enumeration (permutations, Stirling and Bell numbers), recurrences, generating functions, basic asymptotics. Prerequisites: 51 or equivalent.
Terms: Win | Units: 3 | UG Reqs: GER:DB-Math | Grading: Letter or Credit/No Credit

MATH 109: Applied Group Theory

Applications of the theory of groups. Topics: elements of group theory, groups of symmetries, matrix groups, group actions, and applications to combinatorics and computing. Applications: rotational symmetry groups, the study of the Platonic solids, crystallographic groups and their applications in chemistry and physics. Honors math majors and students who intend to do graduate work in mathematics should take 120. WIM.
Terms: Spr | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

MATH 110: Applied Number Theory and Field Theory

Number theory and its applications to modern cryptography. Topics: congruences, finite fields, primality testing and factorization, public key cryptography, error correcting codes, and elliptic curves, emphasizing algorithms. WIM.
Terms: Aut | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

MATH 113: Linear Algebra and Matrix Theory

Algebraic properties of matrices and their interpretation in geometric terms. The relationship between the algebraic and geometric points of view and matters fundamental to the study and solution of linear equations. Topics: linear equations, vector spaces, linear dependence, bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors and eigenvalues; diagonalization. ( Math 104 offers a more application-oriented treatment.)
Terms: Aut, Win, Spr, Sum | Units: 3 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit
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