Linear Algebra and Geometry: Second Course

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In your cart, save the other item s for later in order to get NextDay delivery. We moved your item s to Saved for Later. There was a problem with saving your item s for later. You can go to cart and save for later there. Average rating: 0 out of 5 stars, based on 0 reviews Write a review. Irving Kaplansky. Walmart Tell us if something is incorrect. Book Format: Choose an option. Add to Cart. Product Highlights The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry.

This volume features examples, exercises, and proofs. About This Item We aim to show you accurate product information. Manufacturers, suppliers and others provide what you see here, and we have not verified it. See our disclaimer. Customer Reviews. Write a review. See any care plans, options and policies that may be associated with this product. Email address. As the author describes: it is a book on applicable mathematics which reflects the emphasis of the course. Syllabus: Chapters 1, 2, 3, 4, selected topics from 5, 6, 7 and 8.

Topics include — Fourier series — Orthogonal sets of functions — Boundary value problems in differential equations — Fourier Transform — Laplace Transform. This is an introductory course in convex analysis and optimization, with a focus on applications in data science. Some representative topics include duality, monotone operators, computational complexity, acceleration, splitting methods, stochastic algorithms, and elements of nonsmooth and nonconvex optimization.

This course is appropriate for anyone with a working knowledge of linear algebra and mathematical analysis. Though the course "MATH E: High dimensional probability for data science Autumn " is not a prerequisite, it would help to contextualize the material. The first quarter of this class "Math " will concentrate on Complex Analysis. The second and third quarters of this class "Math and " will be devoted to Real Analysis.

Winter quarter will cover the fundamentals of measure theory and Lebesgue integration. Topics include functions of bounded variation and absolute continuity, the fundamental theorem of calculus, and the Radon-Nikodym theorem. Spring quarter will cover elements of the theory of functional analysis. Combinatorics has connections to all areas of mathematics and many other sciences including biology, physics, computer science, and chemistry. We have chosen core areas of study which should be relevant to a wide audience.

The main distinction between this course and its undergraduate counterpart will be the pace and depth of coverage. In addition we will assume students have a basic knowledge of linear and abstract algebra. We will include many unsolved problems and directions for future research. Every discrete process leads to questions of existence, enumeration and optimization.

This is the foundation of combinatorics. In this quarter we will present the basic combinatorial objects and methods for counting various arrangements of these objects. Grading: Grading will be based on weekly homework. It has deep connections to combinatorics, optimization, number theory, and computer science.

It is also very rich in simple-to-state yet long-unsolved problems. Can the number of i -dimensional faces of a polytope be smaller than both the number of its vertices and the number of its top-dimensional faces? These questions are still open except for a few small values of d. This course will be a sampler of a few of the topics in this vast field. Books: There will be no official textbook.

Instead, we'll use quite a few sources including several recent papers. Some of the textbooks that will be handy are: 1 A course in convexity by Alexander Barvinok, In this course we will discuss some fundamental results on both finite and metric graphs aka abstract tropical curves. We will also present a few open problems along the way, some of which might be within reach for strong undergraduate or graduate students.

We will use various sources, including several research papers. Some of the references for the more classical topics are: 1 Reinhard Diestel, Graph theory , Fifth, Graduate Texts in Mathematics, vol. This is intended to be a one year introduction to algebraic topology. The first two quarters will cover simplicial complexes and CW-complexes; singular, simplicial, and cellular homology; and products and universal coefficient theorems. The third quarter will be devoted to characteristic classes; these are cohomological invariants of vector bundles.

Learning outcomes

We will cover Stiefel-Whitney and Chern classes, as well as cohomology operations and some background information on vector bundles. Applications will be made to the study of manifolds. A lot less is really necessary, so if you haven't completed these sequences, please see me if you are interested in registering for the course. Linear Theory: Solvability, a priori estimates, Schauder and Calderon-Zygmund estimates, and regularity. Monge-Ampere equation, special Lagrangian equations, Bellman equations, and Isaacs equations. The topic of algebraic groups is a rich subject combining both group-theoretic and algebro-geometric-theoretic techniques.

Algebraic groups play an important role in algebraic geometry, representation theory and number theory. In this course, we will take the functorial approach to the study of linear algebraic groups more generally, affine group schemes equivalent to the study of Hopf algebras. The classical view of an algebraic group as a variety will come up as a special case of a smooth algebraic group scheme.

Syllabus for Linear Algebra II

Our algebraic approach will be independent even complementary to the analytic approach taken in the course on Lie groups. Waterhouse and J. We will also reference the classic texts by A. Borel, J. Humphreys and T. Topics at a glance: -Group schemes over an arbitrary base -Affine group schemes vs Hopf algebras; -Representations: modules vs. References: We will use the language of schemes following the excellent introductory texts of W. Our approach will be based partially on the observation due to Weil that every adjoint simple algebraic group of classical type occurs as a connected component of an automorphism group of a central simple algebra with involution.

This will complement the classical approach due to Borel. Topics at a glance: -Infinitesimal theory: differential and Lie algebras of affine group schemes; -Borel fixed point theorem, parabolic subgroups, flag varieties; -Structure theory for split semisimple algebraic groups: maximal tori, root systems, Weyl groups and Dynkin diagrams; -Root datum and classication theorem; -Representations: Highest weight theory if time allows. Waterhouse; 2 Representations of Algebraic Groups, J. Merkurjev, M.

Math Courses

Rost, J-P. Tignol; 4 Algebraic groups: the theory of group schemes of finite type over a field , J. Milne; Linear Algebraic groups, A. Borel; J.

Linear Algebra and Geometry : A Second Course -

Humphreys; T. Springer these are three different books! The course will be suitable for a 2nd year or above graduate student leaning towards an algebra-related field understood broadly: combinatorics, representation theory, algebraic geometry, algebraic topology. The second year graduate algebra course "Algebraic structures" is desirable but not required.

The modern theory of Monge-Kantorovich optimal transport is barely three decades old.

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Already it has established itself as one of the most happening areas in mathematics. It lies at the intersection of analysis, geometry, and probability with numerous applications to physics, economics, and serious machine learning.

Course summary

This year-long graduate topics course will serve as an introduction to this rich and useful theory. The textbooks will be [1] and [2]. This will be supplemented often with papers,especially on the very recent approach by the so-called Schrodinger problem.

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  • We will roughly follow the following outline. Fall: State the transport problem with a general cost function.

    Geometry of Linear Algebra

    Displacement convexity. Special examples.

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