CSD1121 Linear Algebra and Geometry (6 credits)
Prerequisite(s): None
The two main themes throughout the module are vector geometry and linear transformations. Topics from vector geometry include vector arithmetic, dot product, cross product, and representations of lines and planes in three-space. Linear transformations covered include rotations, reflections, shears and projections. Students study the matrix representations of linear transformations along with their derivations. The curriculum also presents affine geometry and affine transformations along with connections to computer graphics. This module also includes a review of relevant algebra and trigonometry concepts.
CSD1251 Calculus and Analytic Geometry 1 (6 credits)
Prerequisite(s): None
This module introduces the calculus of functions of a single real variable. The main topics include limits, differentiation, and integration. Limits include the graphical and intuitive computation of limits, algebraic properties of limits, and continuity of functions. Differentiation topics include techniques of differentiation, optimization, and applications to graphing. Integration includes Riemann sums, the definite integral, anti-derivatives, and the Fundamental Theorem of Calculus.
CSD2201 Calculus and Analytic Geometry 2 (6 credits)
Prerequisite(s): CSD1251
This module builds on the introduction to calculus in CSD1251. Topics in integration include applications of the integral in physics and geometry and techniques of integration. The module also covers sequences and series of real numbers, power series and Taylor series, and calculus of transcendental functions. Further topics may include a basic introduction to concepts in multivariable and vector calculus.
CSD2251 Linear Algebra (6 credits)
Prerequisite(s): CSD2201
This module presents the mathematical foundations of linear algebra, including a review of basic matrix algebra and linear systems of equations as well as basics of linear transformations in Euclidean spaces, determinants, and the Gauss-Jordan Algorithm. The more substantial part of the module begins with abstract vector spaces and the study of linear independence and bases. Further topics may include orthogonality, change of basis, general theory of linear transformations, eigenvalues, eigenvectors, as well as applications to least-squares approximations and Fourier transforms, differential equations, and computer graphics.
CSD2259 Discrete Mathematics (6 credits)
Prerequisite(s): CSD2201
This module gives an introduction to several mathematical topics of foundational importance in the mathematical and computer sciences. Typically starting with propositional
and first order logic, the module considers applications to methods of mathematical proof and reasoning. Further topics include basic set theory, number theory and applications to cryptography, relations, mathematical induction, and basic probability. Other topics may include graph theory, asymptotic analysis, and finite automata.
CSD2301 Motion Dynamics and Lab (6 credits)
Prerequisite (s): CSD1251
This module introduces the various physical laws that describe motions of objects around us. Students learn to internalize concepts involved with kinematics, Newtonian dynamics, work and energy, momentum, rotational motion and condition for the static equilibrium of rigid bodies and develop keen problem solving skills in motion dynamics.
CSD3241 Probability and Statistics (6 credits)
Prerequisite(s): CSD2201
This module is an introduction to basic probability and statistics with an eye toward computer science and artificial intelligence. Basic topics from probability theory include sample spaces, random variables, continuous and discrete probability density functions, mean and variance, expectation, and conditional probability. Basic topics from statistics include binomial, Poisson, chi-square, and normal distributions; confidence intervals; and the Central Limit Theorem. Further topics may include fuzzy sets and fuzzy logic.