2016–2017–A term
Oct 30, 2016Jan 27, 2017 Exam Period Ends: March 10, 2017
Courses
Undergraduate Courses
Fundamentals of Measure Theory (*) Pdf 201.1.0081
Prof. Tom Meyerovitch
יום א 14:00  12:00 בבנין 90 (מקיף ז’) [90] חדר 237
יום ה 14:00  12:00 בבנין 90 (מקיף ז’) [90] חדר 243
Algebras and sigmaalgebras of subsets, the extension theorem and construction of Lebesgue’s measure on the line, general measure spaces, measurable functions and their distribution functions, integration theory, convergence theorems (Egorov’s, relations between convergence in measure and a.e. convergence), the spaces and and their completeness, signed measures, the RadonNikodym theorem, measures in product spaces and Fubini’s theorem.
Theory of Numbers Pdf 201.1.6031
Prof. Eitan Sayag
יום ב 18:00  16:00 בגוטמן [32] חדר 108
יום ד 18:00  16:00 בבנין 90 (מקיף ז’) [90] חדר 239
Number Theory studies the structure of the integers and the natural numbers. In addition to classical topics (prime numbers, congruences, quadratic residues, etc.) there is an emphasis on algorithmic questions and in particular on applications to cryptography.
 Divisibility and prime numbers
 Congruences
 The multiplicative group of
 Quadratic residues
 Continued fractions
 Algebraic numbers and algebraic integers
Algebraic Structures Pdf 201.1.7031
Dr. Ishai DanCohen
יום ב 13:00  11:00 בקרייטמןזלוטובסקי(חדש) [34] חדר 14
יום ה 12:00  10:00 בבנין 90 (מקיף ז’) [90] חדר 134
 Groups, the factor group and the homomorphism theorems, Sylow’s theorems and permutation actions of groups.
 Rings, Integral Domains and Fields. Ideals: maximal and prime. Unique Factorization Domains, Principle Ideal Domains, Euclidean Domains.
 Modules, structure theorems for finitely generated modules over a PID, application to finitely generated abelian groups and to the Jordan Canonical Form.
Infinitesimal Calculus 3 Pdf 201.1.0031
Prof. Uri Onn
יום ד 13:00  11:00 בגוטמן [32] חדר 114
יום א 11:00  09:00 בגוטמן [32] חדר 114
יום ב 14:00  13:00 בגוטמן [32] חדר 206
 Basic concepts of topology of metric spaces: open and closed sets, connectedness, compactness, completeness.
 Normed spaces and inner product spaces. All norms on are equivalent.
 Theorem on existence of a unique fixed point for a contraction mapping on a complete metric space.
 Differentiability of a map between Euclidean spaces. Partial derivatives. Gradient. Chain rule. Multivariable Taylor expansion.
 Open mapping theorem and implicit function theorem. Lagrange multipliers. Maxima and minima problems.
 Riemann integral. Subsets of zero measure and the Lebesgue integrability criterion. Jordan content.
 Fubini theorem. Jacobian and the change of variables formula.
 Path integrals. Closed and exact forms. Green’s theorem.
 Time permitting, surface integrals, Stokes’s theorem, Gauss’ theorem
Logic Pdf 201.1.6061
Dr. Assaf Hasson
יום ב 16:00  14:00 בבנין 90 (מקיף ז’) [90] חדר 136
יום ג 12:00  10:00 בגוטמן [32] חדר 114
 An axiom system for predicate calculus and the completeness theorem.
 Introduction to model theory: The compactness Theorem, Skolem–Löwenheim Theorems, elementary substructures.
 Decidability and undecidability of theories, Gödel first Incompleteness Theorem.
Graph Theory Pdf 201.1.6081
Prof. Shakhar Smorodinsky
יום ב 16:00  14:00 בצוקר, גולדשטייןגורן [72] חדר 115
יום ג 12:00  10:00 בגולדברגר [28] חדר 301
Graphs and subgraphs, trees, connectivity, Euler tours, Hamilton cycles, matching, vertex and edge colorings, planar graphs, introduction to Ramsey theory, directed graphs, probabilistic methods and linear algebra tools in Graph Theory.
Probability Pdf 201.1.8001
Prof. Ariel Yadin
יום ב 11:00  09:00 ב [90] חדר 238
יום ד 11:00  09:00 בגולדברגר [28] חדר 203
An introduction to the basic notions of probability theory:
sample spaces limits of events conditional probability independent events sigma algebras, continuous spaces, Lebesgue measure random variables and distributions independence expectation variance and covariance convergence of random variables: almostsure, in Lp, in probability law of large numbers convergence in law central limit theorem
Ordinary Differential Equations Pdf 201.1.0061
Prof. Victor Vinnikov
יום א 16:00  14:00 בגוטמן [32] חדר 114
יום ג 14:00  12:00 בצוקר, גולדשטייןגורן [72] חדר 123
Ordinary differential equations of first order, existence and uniqueness theorems, linear equations of order n and the Wronskian, vector fields and autonomous equations, systems of linear differential equations, nonlinear systems of differential equations and stability near equilibrium
Graduate Courses
Basic Concept in Toplogy and Geometry (#) Pdf 201.2.5221
Prof. Michael Levin
יום א 16:00  14:00
יום ג 12:00  10:00
 Topological manifolds. The fundamental group and covering spaces. Applications.
 Singular homology and applications.
 Smooth manifolds. Differential forms and Stokes’ theorem, definition of deRham cohomology.
 Additional topics as time permits.
Basic concepts in Modern Analysis (#) Pdf 201.2.0351
Dr. Daniel Markiewicz
יום א 16:00  14:00
יום ג 14:00  12:00
This course will cover the fundamentals of Functional Analysis, including Hilbert spaces, Banach spaces, and operators between such spaces.
Lie Groups Pdf 201.2.4141
Prof. Uri Onn יום ב 18:00  15:00 בגרוסמן/ דייכמן [58] חדר 101
 Review of differentiable manifolds, definition of a Lie group. Quotients in the category of Lie groups, homogeneous manifolds, haar measure, connected components.
 Algebraic groups, matrix groups, the classical groups.
 Lie algebras and connection to Lie groups.
 Nilpotent, solvable and semisimple Lie algebras and Lie groups, Lie theorem, Engel theorem, Levi decomposition.
 CartanKilling form.
 Representation of a Lie algebra over the complex numbers.
 Root and weights, root systems, Dynkin diagrams, classication of complex semisimple Lie algebras.
padic analysis Pdf 201.2.0131
Prof. Eitan Sayag
Mon 14:00–16:00
Wed 12:00–13:00
Wed 14:00–15:00
I plan to cover Bernstein’s Harvard notes on adic groups but I will try to emphasize applications of the theory to analysis on adic spaces and adelic spaces.
Topics:

Review of material from past semesters (the courses “Derived Categories I and II”).

Derived categories in commutative algebra: dualizing complexes, Grothendieck’s local duality, MGM Equivalence, rigid dualizing complexes.

Derived categories in algebraic geometry: direct and inverse image functors, global Grothendieck duality, applications to birational geometry (survey), adic cohomology and PoincareVerdier duality (survey), perverse sheaves (survey).

Derived categories in noncommutative ring theory: dualizing complexes, tilting complexes, derived Morita theory.

Derived algebraic geometry: nonabelian derived categories (survey), infinity categories (survey), derived algebraic stacks (survey), applications (survey).
Notes
 Courses marked with (*) are required for admission to the M.Sc. program in Mathematics.
 The M.Sc. degree requires the successful completion of at least 2 courses marked (#). See the graduate program for details
 The graduate courses are open to strong undergraduate students who have a grade average of 85 or above and who have obtained permission from the instructors and the head of the teaching committee.
 Please see the detailed undergraduate and graduate programs for the for details on the requirments and possibilities for complete the degree.