Announcements
MCS ANNOUNCES NEW COURSES TO BE OFFERED IN 2009/2010!
STA313H5 Topics in Statistics: Introduction to limiting laws
Plan of the course and learning objectives: In the first part of the course, we will study limiting laws in the simplest possible setting of finite probability spaces. In this setting, the technicalities are reduced to the absolute minimum. As a result, the students will be able to quickly and efficiently understand the heart of the matter and to start developing probabilistic intuition. In the second part of the course we will revisit the notions from the first part, this time within the general framework of measure theory. This part will be technically more challenging and we will be able to prove stronger results. The students will learn the language of modern probability as well as some important techniques of proof, which will be very useful for their future studies.
Main topics of the course:
- Basic notions of probability theory
- Concentration inequalities
- Law of large numbers
- Central limit theorem
- Elementary measure theory and integration
- The different notions of convergence
- Selected topics
Instructor: Eugene Kritchevski
MAT478FH5 Topics in Mathematics: Introduction to Mathematics of Finance
Want to understand what went wrong with the financial markets?
In the Fall term of 2009 the Department of Mathematical and Computational Sciences at UTM will offer a course on Mathematics of Finance, as a course on Topics in Mathematics, MAT 478FH5.
Pre-requisites: MAT223H5, MAT232H5/MAT233H5, STA257H5
Course description: This course introduces a range of mathematical concepts and techniques of mathematical finance. We will consider mostly discrete time models for the price dynamics of actively traded assets such as stocks, and develop the basic principles of risk-neutral valuation of contingent claims such as call and put options. Specific topics studied include: one-period and multi-period binomial tree models; the Black and Scholes model; self-financing replicating portfolios; martingales and conditional expectation; risk-neutral valuation in the absence of arbitrage; option deltas, gammas, vegas and other sensitivities. If time permits we will also discuss options on currencies and interest rates, and possibly describe some continuous time models for asset prices. Students are expected to have a solid background in calculus, familiarity with matrices and basic linear algebra, and knowledge of basic discrete and continuous probability distributions. Prior experience with stochastic processes is a plus but is not necessary. No knowledge of business or finance is required, other than a basic understanding of compound interest.
Textbook: M. Baxter, A. Rennie, Financial Calculus. An introduction to derivative pricing., Cambridge Univ. Press.
Instructor: Dr. Tom Alberts
Direct all inquiries to the MCS Undergraduate Counselor
MAT 309H5 Introduction to Mathematical Logic
The two most important concepts of pure mathematics are "truth" and "provability". Do you agree? Perhaps you think
THIS STATEMENT IS FALSE.
Is it? Thinking about this paradox led Kurt Godel to perhaps the greatest achievement in 20th century mathematics, distinguishing truth and provability. The techniques he developed also led to the invention of the computer and the theory of recursive functions. In this course we shall go through his famous proof and sketch other developments in mathematical logic.
Prerequisite: MAT 102H5, MAT 202H5. Note: the course prerequisites will change to MAT 102H5, MAT 202H5, effective 2009/10. Students without MAT 202H5 may seek permission of the instructor.
MAT 378H5 Introduction to Real Analysis
Do you want to really UNDERSTAND what you have learned in Calculus? Do you want to really get acquainted with the exciting world of Modern Analysis? Do you want to learn about the Fourier Series, an important tool in Engineering, Physics, Chemistry, and Economics? MAT378 is completely revised for this year. Come and learn REAL Analysis!
Note: the course description has changed to match MAT 337 at St George. The new description reads: Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.
MCS DEPARTMENT ANNOUNCES NEW COURSES IN COMPUTER SCIENCE, MATHEMATICS AND STATISTICS TO BE OFFERED IN 2008/09! 24/06/08
CSC404H5 Video Game Design - An introduction to the concepts and techniques for the design and development of electronic games. Topics include: game history, social issues and story elements. The software engineering, artificial intelligence and graphics elements for video games. Level and model design. Audio elements. Real-world aspects of the gaming industry, including the business of game development, design teams and game promotion. Assignments test practical skills in game development, with a team implementation of a complete video game as a course project. [26L, 13P]
Prerequisite: CSC290H5 Two of (CSC301H5, CSC318H5, CSC384H5, CSC418H1)
CSC488H5 Compilers and Interpreters - Compiler organization, compiler writing tools, use of regular expressions, finite automation and content-free grammars, scanning and parsing, runtine organization, semantic analysis, implementing the runtime model, storage allocation, code generation. [26L, 13T]
Prerequisite: CSC263H5/378H5, 290H5, 324H5, 258H5
Recommended Preparation: CSC209H5
MAT233H5 Calculus of Several Variables -
"Bridging Course"; accepted as prerequisite for upper level courses in replacement of MAT232H5. Limited Enrolment.
Sequences and series, power series, Taylor series, trigonometric and inverse trigonometric functions and their use in integrations. Differential and integral calculus of several variables; partial differentiation, chain rule, extremal problems, Lagrange multipliers, classification of critical points. Multiple integrals, Green's theorem and related topics. [52L, 13T]
Exclusion: MAT138Y5, 232H5
Prerequisite: MAT134Y5/135Y5/137Y5 or 80% in MAT133Y5
Limited enrolment; preference given to students enrolled in MAT programs.
MAT401H5 Polynomial Equations and Fields - a follow-up course to MAT301H5, with further study of algebraic structures. The striking consequences of Galois theory: the impossibility of trisecting an angle via a ruler and compass construction, and the nonexistence of a formula for finding the roots of a fifth degree equation.
Calendar Description: Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extentions, adjunction of roots of a polynomial. Constructibiliy, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals. [39L, 13T]
Exclusion: MAT392H5 in 2006/2007.
Prerequisite: MAT102H5, 224H5, 232H5, 301H5.
Offered in alternate years. With instructor's permission, may be taken as a reading course.
MAT406H5 Mathematical Introduction to Game Theory - A subject originated by mathematicians (especially von Neumann and Nash) with many applications in the social sciences. Note: MAT102H should have been listed as a prerequisite for this course.
Calendar Description: Combinatorial games: Nim and other impartial games; Sprague-Grundy value; existence of a winning strategy in partisan games. Two-player (matrix) games: zero-sum games and Von-Neuman's minimax theorem; general sum-matrix games, prisoner's dilemma, Nash equilibrium, cooperative games, asymmetric information. Multi-player games: coalitions and the Shapley value. Possible additional topics: repeated (stochastic) games; auctions; voting schemes and Arrow's paradox. Mathematical tools that may be introduced include hyperplane separation of convex sets and Brouwer's fixed point theorem. Numerous examples will be analyzed in depth, to offer insight to the mathematical theory and its relation with real life situations. [39L, 13T]
Prerequisite: MAT2235, STA257H5
Offered in alternate years. With instructor's permission, may be taken as a reading course.
STA431H5 Structural Equation Models - Random vectors and matrices, univariate and multivariate regression with measurement error, latent variables, model identification, the LISREL model, path analysis, confirmatory factor analysis, longitudinal data analysis, robustness of the normal model. A statistical computing package will be used. [39L, 13T]
Prerequisite: STA331H5/ECO327Y5
Offered in alternate years.
DEAN ANNOUNCES NEW MCS DEPARTMENT CHAIR
TO: Faculty, Staff and Students in the Department of Mathematical and Computational Sciences
FROM: Gage Averill, Vice-Principal Academic and Dean
DATE: April 10th, 2008
RE: Announcement re. Chair of the Department of Mathematical and Computational Sciences
I am pleased to announce that Professor Konstantin Khanin has agreed to serve for a five year term as Chair of the Department of Mathematical and Computational Sciences, commencing on July 1st, 2008 to June 30th, 2013.
This appointment has been approved by the Agenda Committee of the Academic Board at its meeting on April 9th.
Please join me in extending warm congratulations to Konstantin on his appointment and in thanking him in advance for his service to the University, UTM and the Department. I would also like to express my appreciation to the Search Committee for their dedicated contributions to this appointment.
NOTICE REGARDING HOTMAIL ACCOUNTS
Hotmail has blocked any incoming/outgoing email from the University of Toronto. Faculty and staff are unable to respond to email accounts that are from hotmail. We ask students to please use their University of Toronto accounts at this time.
