This course is an introduction to numerical Linear Algebra. Topics include: matrix factorizations: QR-factorization, Cholesky factorization , vector and matrix norms: properties of the ‖.‖1, ‖.‖2|| and ‖.‖ norms of vectors in Rn, properties of the ‖.‖1, ‖.‖2|| , ‖.‖ and ‖.‖F norms of an mxn matrix, condition number of a matrix, ill-conditioned systems, the Hilbert matrix, perturbation analysis of linear systems, singular value decomposition (SVD) of an mxn matrix, Moore-Penrose inverse, rank k approximation of a matrix, applications of the SVD to least-squares problems, iterative methods for large sparse linear systems: the Jacobi and Gauss-Seidel methods, the SOR method, applications to the solution of linear systems with banded coefficient matrices, regularization methods for ill-conditioned linear systems, regularization of orders 0, 1 and 2, and the L-curve method for choosing an optimal regularization parameter.
This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include unconstrained optimization: optimality conditions, Newton's method, quasi-Newton's methods, Steepest Descent Method, Conjugate-Gradient methods, Line Search methods, Trust Region Methods, Derivative-Free Methods, constrained Optimization: optimality conditions for (a) linear equality constraints, (b) linear inequality constraints, (c) nonlinear constraints, feasible-point methods, sequential quadratic programming (SQP), reduced-gradient method, penalty and barrier methods.
This course will examine applications of mathematics in biological contexts including genetics, ecology, physiology, neuroscience and epidemiology. Topics include variants of the MSEIRS epidemic models, disease-free and endemic equilibrium points, determination of the basic reproduction number using the next-generation matrix approach, local stability and global stability analysis of equilibrium points and case studies : HIV/AIDS, TB and Vector-Host Models including Malaria. Further topics are parameter estimation for selected epidemic models, simulation and prediction.
This is the second of two courses designed to equip students with pedagogical content knowledge to enable them teach new or perceived difficult topics in the senior high school chemistry syllabus more competently in a variety of ways to reflect students’ different learning styles. Students will be able to develop special amalgam of content and pedagogy that is uniquely the province of teachers.
Appropriate strategies for successful teaching of selected topics, generally, will be discussed. Students will also learn how to recognize opportunities where learners will be encouraged to develop their thinking skills as applied to the study of chemistry.
This course introduces the basic theories and methodologies of digital image processing. The topics include manipulating images in MATLAB/OCTAVE, images as Arrays of Numbers, digital image, compression the singular value decomposion, the image de-blurring problem: a mathematical model of the blurring process. Further topics include de-blurring using a general linear model, obtaining the point spread function (PSF). De-bluring images using TSVD method, total variation method, and the Tikhonov regularization method, general image reconstruction as an inverse problem.
This course introduces students to an in-depth study of the function and structural moiety of organic macromolecules of biological relevance. Topics to be discussed in this course will revolve around classification of carbohydrates, stereoisomerism in carbohydrates, polyfunctional chemistry of simple sugars, cellulose and its derivatives, enzymatic glycogen hydrolysis, conversion of ATP to ADP, and proteins (Classification, amino acids, peptides, determination of protein structure), nucleic acids, nucleosides, nucleotides, and synthetic polymers.
This course focuses on partial differential equation (PDE) models, which will be developed in the context of modelling heat and mass transport and, in particular, wave phenomena, such as sound and water waves. This course develops students' skills in the formulation, solution, understanding and interpretation of PDE models. Topics include classical theory of partial differential equations together with the modern theory based on functional analysis; systems of partial differential equations, boundary value problems, stability and convergence; applications to the classical problems of mathematical physics.
The course will expose students to preparation of standard reagents and inorganic complexes. Other experiments will focus on determination of heat of combustion, phase rules and concepts related to chemical kinetics. The use of other analytical methods such gravimetric methods, complexometric titrations, electrochemical and spectroscopic methods will be performed.
This course is intended to give students an insight into the principles governing how and why organic chemical reactions take place, as well as, the survey of preparative methods in organic chemistry and their application to the synthesis of complex molecules. It will largely focus on the development of novel synthetic methods and applications of these in target synthesis, most often either natural products or biologically active compounds of pharmaceutical or agrochemical significance. Nucleophilic, electrophilic, elimination and addition reactions will also be covered
This course provides advanced topics in complex analysis such as conformal mappings, and physical applications of conformal mapping. Further topics include analytic continuation and Riemann surfaces, Rouches’s theorem and principle of the argument, mapping properties of analytic functions, inverse function theory, maximum modulus theory, infinite products and gamma function, Sterling’s formula and Bessel’s functions, homotopy and homology theory, and analytic properties of holomorphic functions.