University of Cape Town

Study the fundamentals of real analysis, including Axioms of the real numbers, supremum and infimum; Countable sets; Sequences and series; Open and closed sets, compactness; Limits, continuity, differentiability; Sequences and series of functions, uniform convergence, power series; Integration. Please note that lectures alternate during the week so that students can take any of MAM2012S, MAM2013S and MAM2014S concurrently.

This course provides an intermediate level introduction to the application of modern time series methods that may be used to analyze economic data. The initial part of the course includes a review of techniques that can be used to identify the dynamic properties of time series data. Thereafter, a selection of the popular modelling frameworks is introduced (i.e. autoregressive integrated moving average models, distributed lag models, and vector autoregressive models). Extensions to these frameworks, which allow for aspects such as cointegration and error correction representations, are also covered, before attention is directed towards the application of model misspecification tests and forecasting exercises. Course entry requirements: ECO4006F, ECO4007F and ECO4016F.

This course introduces the language and methods of the area of Discrete Mathematics and show how discrete mathematics can be used in modern computer science (with the focus on algorithmic applications). Topics covered include (1) sets, relations and functions; (2) basic logic, including propositional logic, logical connectives, truth tables, propositional inference rules and predicate logic; (3) proof techniques, including the structure of mathematical proofs, direct proofs, disproving by counterexample, proof by contradiction; (4) basics of counting, including counting arguments, the pigeonhole principle, permutations and combinations, solving recurrence relation; (5) graphs and trees; (6) discrete probability, including finite probability space, axioms of probability, conditional probability; and, (7) linear algebra, including vectors, matrices and their applications. The course is offered in a blended-learning format. Students are provided with a set of video lectures that they can watch multiple times. Student contact time is in a tutorial format aimed at reinforcing the principles introduced in the online lectures and giving students time to do exercises under the supervision of tutors. Co-requisites: MAM1004S or MAM1005H (unless a pass has been obtained for MAM1004F or MAM1031F or equivalent).

 Study the fundamentals of abstract algebra and number theory, including induction, strong induction and Well-Ordering axiom; Divisibility and prime factorization; Modular arithmetic; Permutations; Groups, Subgroups, Cyclic groups; Isomorphisms; Simple groups, Factor groups, Lagrange's Theorem; The First Isomorphism Theorem. Please note that lectures alternate during the week so that students can take any of MAM2012S, MAM2013S and MAM2014S concurrently. Course entry requirements: MAM1031F and MAM1032S or equivalent.

The course is a continuation of Initial Spanish A and provides a further practical knowledge of spoken and written Spanish. There is no in-depth study of literature at this level. The module focuses on the consolidation of language skills in reading, writing, listening, and the introduction of conversational skills. By the end of this second semester, students engage in interactions with Spanish speakers in socially and culturally appropriate forms without problems. DP requirements: At least 80% attendance at lectures, tutorials, and language laboratory sessions; completion and timeous submission of all written assignments; attendance at all scheduled tests, written and oral examinations. Assessment: Coursework (homework, tests and labs) (40%); two-hour written examination (40%); oral examination (20%). 

Building on the theoretical constructs and skills of earlier courses, students are introduced to Community Development from a political economy of welfare perspective. This course uses youth development and contemporary issues as a lens for learning about community assessment and intervention strategies. The course provides the basic concepts, theory, processes and skills required for culturally appropriate assessment of systems and situations at community level, and community development as a strategy of interaction within a framework of youth and youth development in South and Southern Africa. Course entry requirements: At least second-year status.

This course develops an understanding of the causes and motivations of personal travel, the means by which movement takes place, as well as the impact personal travel, freight and transport infrastructure have on the environment, economy, and society. This is done by providing a grounding in techniques for modelling, analyzing and assessing (multi-modal) transport systems and their impacts. Transport policy and appraisal and fundamentals of data collection, as well as professional communication (presentation skills) are included. Course entry requirements: None. Co-requisites: None. 

This course surveys the history and contemporary practice of public administration (or public bureaucracies) around the world. Some of the key questions that are answered include what is the proper place and role of public administration in a democracy? What are the benefits and potential risks of public administration in democratic government? What impact does public administration have on our lives as citizens? How can we construct effective working relationships between elected politicians and unelected administrators. And finally, what role can public administration play in responding to global policy crisis? Although this course adopts a comparative perspective, particular attention is paid to the role that public administration has played in democratic transitions in South and Southern Africa. Course entry requirements: POL1004F and POL1005S.

This course pays special attention to issues of theory and method in the psychology of religion, in order to develop an understanding of personal identity, as well as mental and spiritual health in religious contexts. While recognizing the importance of gender, class, race, ethnicity and other social forms of identity, the course focuses on religious dynamics of personal identity and the formation of selfhood through case studies in consciousness, mysticism, embodiment, intertextual reading practices and cultural resources for being human. The course explores the various ways in which religion might inform personal, social and intersubjective notions of self, while providing conception of the good/the good life. Course entry requirements: Second-year status.

This course forms part of the third-year major in Applied Statistics. It is an introduction to the study of Operational Research (OR) and explores fundamental quantitative techniques in the OR armamentarium with a strong focus on computer-based application. The course is intended for students in the applied statistics stream but may be taken as an elective by students in the mathematical statistics stream. Topics covered include linear and non-linear programming where students will learn to find optimal solutions by characterizing problems in terms of objectives, decision variables and constraints, decision making under uncertainty through decision trees, decision rules and scenario planning, Queueing Theory simulation through modelling the operation of real-world systems as they evolve over time. Course entry requirements: STA2030S or STA2005S; STA3030F is recommended.