printer friendly pageMATH 77Q: Probability and gambling
One of the earliest probabilistic discussions was in 1654 between two French mathematicians, Pascal and Fermat, on the following question: 'If a pair of six-sided dice is thrown 24 times, should you bet even money on the occurrence of at least one `double six'?' Shortly after the discussion, Huygens, a Dutch scientist, published De Ratiociniis in Ludo Aleae (The Value of all Chances in Games of Fortune) in 1657; this is considered to be the first treatise on probability. Due to the inherent appeal of games of chance, probability theory soon became popular, and the subject underwent rapid development in the 18th century with contributions from mathematical giants, such as Bernoulli, de Moivre, and Laplace. There are two fairly different lines of thought associated with applications of probability: the solution of betting/gambling and the analysis of statistical data related to quantitative subjects such as mortality tables and insurance rates. In this Introsem, we will discuss poker and
more »
One of the earliest probabilistic discussions was in 1654 between two French mathematicians, Pascal and Fermat, on the following question: 'If a pair of six-sided dice is thrown 24 times, should you bet even money on the occurrence of at least one `double six'?' Shortly after the discussion, Huygens, a Dutch scientist, published De Ratiociniis in Ludo Aleae (The Value of all Chances in Games of Fortune) in 1657; this is considered to be the first treatise on probability. Due to the inherent appeal of games of chance, probability theory soon became popular, and the subject underwent rapid development in the 18th century with contributions from mathematical giants, such as Bernoulli, de Moivre, and Laplace. There are two fairly different lines of thought associated with applications of probability: the solution of betting/gambling and the analysis of statistical data related to quantitative subjects such as mortality tables and insurance rates. In this Introsem, we will discuss poker and other games of chance, such as daily fantasy sports, from the perspective of risk analysis. This Introsem does not require any programming knowledge, but some experience with Excel, MATLAB, R, and/or Python will enhance your experience in our discussion of daily fantasy sports. Students should be familiar with all material from
Math 51. No prior knowledge of sports and games of chance is required. Students must apply through the IntroSem application process.
Terms: Win, Spr
| Units: 3
| UG Reqs: WAY-FR
Instructors:
Kim, G. (PI)
MATH 87Q: Mathematics of Knots, Braids, Links, and Tangles
Preference to sophomores. Types of knots and how knots can be distinguished from one another by means of numerical or polynomial invariants. The geometry and algebra of braids, including their relationships to knots. Topology of surfaces. Brief summary of applications to biology, chemistry, and physics.
Terms: Spr
| Units: 3
| UG Reqs: WAY-FR
Instructors:
Wieczorek, W. (PI)
MATH 104: Applied Matrix Theory
Linear algebra for applications in science and engineering. The course introduces the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and nearly all quantitative fields of science and engineering. While the choice of topics is motivated by their use in various disciplines, the course will emphasize the theoretical and conceptual underpinnings of this subject. Topics include orthogonality, projections, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares methods, and algorithms for solving systems of linear equations; applications include clustering, principal component analysis and dimensionality reduction, regression.
MATH 113 offers a more theoretical treatment of linear algebra.
MATH 104 and
ENGR 108 cover complementary topics in applied linear algebra. The focus of
MATH 104 is on algorithms and concepts; the focus of
ENGR 108 is on a few linear algebra concepts, and many applications. Prerequisites:
MATH 51 and programming experience on par with
CS 106A.
Terms: Aut, Win, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Candes, E. (PI)
;
Cortinovis, A. (PI)
;
Cheng, R. (TA)
...
more instructors for MATH 104 »
Instructors:
Candes, E. (PI)
;
Cortinovis, A. (PI)
;
Cheng, R. (TA)
;
Goyal, S. (TA)
;
Malhotra, A. (TA)
;
Nehme, G. (TA)
;
Park, J. (TA)
;
Tse, D. (TA)
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: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Vondrak, J. (PI)
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; dual space and dual basis; eigenvectors and eigenvalues; diagonalization. Includes an introduction to proof-writing. (
Math 104 offers a more application-oriented treatment.) Prerequisites:
Math 51
Terms: Aut, Win, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Malinnikova, E. (PI)
;
Swaminathan, M. (PI)
;
Vondrak, J. (PI)
...
more instructors for MATH 113 »
Instructors:
Malinnikova, E. (PI)
;
Swaminathan, M. (PI)
;
Vondrak, J. (PI)
;
Amar, S. (TA)
;
Niu, J. (TA)
MATH 115: Functions of a Real Variable
The development of 1-dimensional real analysis (the logical framework for why calculus works): sequences and series, limits, continuous functions, derivatives, integrals. Basic point set topology. Includes introduction to proof-writing. Prerequisite:
Math 51 or
Math 56.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 118: Mathematics of Computation
Notions of analysis and algorithms central to modern scientific computing: continuous and discrete Fourier expansions, the fast Fourier transform, orthogonal polynomials, interpolation, quadrature, numerical differentiation, analysis and discretization of initial-value and boundary-value ODE, finite and spectral elements. Prerequisites:
MATH 51 and 53.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Cortinovis, A. (PI)
MATH 120: Groups and Rings
Recommended for Mathematics majors and required of honors Mathematics majors. A more advanced treatment of group theory than in
Math 109, also including ring theory. Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM course. Prerequisite:
Math 51 and some prior proof-writing experience.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
MATH 122: Modules and Group Representations
Modules over PID. Tensor products over fields. Group representations and group rings. Maschke's theorem and character theory. Character tables, construction of representations. Prerequisite:
Math 113 and 120.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Taylor, R. (PI)
MATH 145: Algebraic Geometry
An introduction to the methods and concepts of algebraic geometry. The point of view and content will vary over time, but include: affine varieties, Hilbert basis theorem and Nullstellensatz, projective varieties, algebraic curves. Required: 120. Strongly recommended: additional mathematical maturity via further basic background with fields, point-set topology, or manifolds.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Zhang, Z. (PI)
Filter Results: