- Lecturer: Duaine Lewis
Calculus and Analytical Geometry/Preliminary Mathematics II
- Complex numbers,
- Analysis, and
Sets and Number Systems
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.
- Lecturer: Peter Chami
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.
Real Analysis 1
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.
- Lecturer: Peter Chami
Statistics for Graduates I
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 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.
- Composition (language), in literature and rhetoric,
producing a work in spoken tradition and written discourse, to
include visuals and digital space
- Composition (music), an original piece of music and its creation
- Composition (visual arts), the plan, placement or arrangement of the elements of art in a work
- Composition (dance), practice and teaching of choreography
- Function composition (mathematics), an operation that takes functions and gives a single function as the result
- Composition of relations (mathematics), an operation that takes relations and gives a single relation as the result
- Composition (combinatorics), a way of writing a positive integer as a sum of positive integers
- Composition algebra (mathematics), an algebra over a field with composing norm
- Binary function or law of composition