M＆S-UWI

1. Complex numbers,
2. Analysis, and
   
3. Matrices.
   

To fully understand mathematics, the essential rules of logic for the formulation of mathematical proofs have to be studied. The various types of mathematical proofs are discussed, mainly using examples in elementary set theory and number systems.

In this course, students are introduced to the basic operations that are performed on sets. In so doing the concepts of relations, functions and binary operations are examined. Next we examine natural numbers and the derived principle of mathematical induction. We discuss permutations, combinations and sequences that are defined recursively with respect to natural numbers. The properties of the integers such as divisibility, greatest common divisor and Euclidean algorithm are examined. We study the field axioms in relation to rational numbers. We solve linear and non-linear inequalities involving the real numbers.

In a broad sense, calculus is the mathematical study of change consisting of differential calculus (concerning rates of change and slopes of curves) and integral calculus (concerning accumulation of quantities and the area under/between curves).

The course continues the study of the fundamental concepts of the differential and integral calculus of a single variable. The used approach is intuitive and informal but nevertheless prepares students to understand the rigorous proofs at a subsequent level. While there is a considerable overlap with the ideas encountered in Calculus A, a greater emphasis is put on the fundamental ideas involved in differentiation and integration. The main results are derived and illustrated although often heuristic proofs are used. 

This course will treat the limits, continuity and differentiability of a function of a single variable from a more rigorous point of view. Double integrals are introduced and methods for their evaluation are considered.

This course exposes students to rigorous mathematical definitions of limits of sequences of numbers and functions, classical results about continuity and series of numbers and their proofs. A major emphasis is placed on the proper use of definitions for the rigorous proof of theorems. The following topics will be covered: The real number system, topological properties of real numbers, sequences, continuity and uniform continuity.

This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable. Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing. However, the concepts introduced in complex analysis are nowadays also ubiquitous in number theory and combinatorics.

Students will calculate line integrals, and the techniques they will learn in this course will help them get past many of the seeming “dead ends” they ran up against in calculus. Indeed, most of the definite integrals they will learn to evaluate cannot be solved except through techniques from complex analysis.

This course will familiarize graduate students who have no understanding of statistics with the rudiments of statistical theory and hopefully, ready them for effective academic and professional practice in the process of statistical research. Primary topics include Graphing and Summarizing Data, Probability, Estimation, Hypothesis Testing, Regression and ANOVA.

These topics will be carried out over 12 lecture Modules which will take place over the next 12 weeks. The student will have to do computer labs where there will have to learn the statistical computer software called R. There will also be 6 quizzes which the student must pass.

On the completion of this course students will should have the ability to perform the rudiment of high‐level application and analysis, particularly in the areas of Biological and Chemical research.

Its the purpose and goal of this course to align itself with the stated policy of the University of the West Indies and the Department of Computer Science, Mathematics and Computer Science to produce graduates who are well versed in the practice of their disciplines in the workforce.

The Math Clinic is an online math tutoring center for students in the first year courses MATH1141 Introductory Linear Algebra & Analytical Geometry and MATH190 Calculus A in the first semester, and MATH1152 Sets and Number Systems and MATH1195 Calculus B in the second semester.

The Math Clinic opens in the second half of the semester and runs to just before the final examination period. Each week a number of tutorial hours are offered where a tutor explains typical math questions of first year courses. Students can submit question to go through, and vote which time slots should be offered each week.  

The course will formally teach MPhil and PhD students how to prepare an extensive review of the literature pertaining to a scientific topic. This will guide students on how to study and evaluate the literature on a given topic and write a comprehensive essay on it. The course will also demonstrate the use of pertinent search engines, discipline-specific traditional reference sources, as well as software for managing reference lists and creating bibliographies.

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