Courses

Sequences of functions. Pointwise and uniform convergence. Power series. The contraction mapping theorem and application. Real analysis. Definition of integral and condition for integrability. Proof of the fundamental theorem of calculus and   major...

Functions of several variables, partial derivative. Directional derivative, gradient. Local extema, constrained extrema. Lagrange multipliers. The gradient, divergence and curl operators. Line, surface and volume integrals. Green's theorem, divergence...

Subgroups, cyclic groups.The Stabilizer-Orbit theorem.Lagrange's theorem. Classifying groups. Structural properties of a group. Cayley's theorem. Generating sets.  Direct products. Finite abelian groups. Cosets and the proof of Lagrange's...

Normed vector spaces.  Limits and continuity of maps between normed vector spaces.  The algebra of continuous functions. Bounded sets of real numbers.  Limit of a sequence. Subsequences.  Series with positive terms.Convergence tests....

Spanning sets. Subspaces, solution spaces. Bases. Linear maps and their matrices.   Inverse maps. Range space, rank and kernel. Eigenvalues and eigenvectors. Diagonalization of a linear operator. Change of basis. Diagonalizing matrices....

Differential forms of 2 and 3 variables. Exactness and integrability conditions. Existence and uniqueness of solution. Second order differential equations with variable coefficients. Reduction of order, variation of parameters. Series solution. Ordinary and...

Introductory Programming for Computational Mathematics
Variables, functions, arrays and matrices, classes, introduction to Graphical User Interfaces (GUI's). Introduction to symbolic computing. Visualization in mathematics.
 

Equivalences, partial order. Construction of R from Z. Elementary number theory. Axiomatically defined systems; groups, rings and fields. Morphisms of algebraic structures. Vector spaces. Homomorphism of vector spaces.
 

Second derivative of a function of a single variable. Applications of first and second derivatives. Hyperbolic and inverse hyperbolic functions. Methods of integration. Applications of the definite integral. Ordinary differential equations, first order and...

1-dimensional kinematics. Forces acting on a particle. 1-dimensional dynamics. Newton's laws of motion; motion under constant acceleration, resisted motion, simple harmonic motion. 3-dimensional kinematics. Relative motion. 2-dimensional motion under...