# Regent School of Informatics & Engineering

### SIMS 1434 Pre-Calculus

This course is designed primarily to equip the students with the fundamental aspects of mathematics that will enable them to pursue differential and integral calculus of single variable. The pre-calculus course encourages the students to perform thorough investigations of mathematical ideas by using numerical, graphical, and algebraic methods. It incites the students to think conceptually so that they can apply the skills obtained from the course to tackle real life situations.

### SIMS 1533 Limits and Derivatives

Limits, tangent lines and derivatives. Applications of the derivative to rates, extrema and curve sketching. The definite integral and its application to determining area.

### SIMS 1543 Logarithms, Integration and Coordinates

Exponentials and logarithms, techniques of integration, volumes and arc length, indeterminate forms, improper integrals, polar coordinates.

### SIMS 1553 General Linear Algebra & Calculus for Business and Economics

Linear equations and their graphs. Systems of linear equations and linear inequalities. Polynomial, exponential and logarithm functions. Vector and matrix algebra, derivatives and optimization. Applications to business and economics are integrated throughout the course. Emphasis is on understanding how problems are formulated mathematical and on interpretation of mathematically expressed real world problems.

### SIMS 1572 Algebra

The course covers both matrix and linear algebra. Systems of linear equations, matrices, determinants, vectors in two and three dimensions, row deductions and echelon forms, LU decomposition. Attention will also be given to linear independence and span, linear transformations, multi-linear functions, vector spaces and subspaces, eigenvectors, the characteristic polynomial, applications.

### SIMS 1623 Discrete and Continuous Mathematics

This course gives an understanding and uses (abstract) discrete structures that are backbone of computer science. Logic: Truth tables, TIF and 1/0 notation, Binary numbers and strings, gates, logic equations and their simplification; Sets: subsets, unions and intersections; Relations and functions: arithmetic modulo powers of 2, look up tables, 1-1 maps, Onto maps, bijection and data bases; Induction and recursion: functions defined by recursive relationships, loops; Graph and tree theory: applied to networks; Algorithms: filtering, interpolation, Euclid’s algorithm; Permutations and combinations: discrete probability, relevance to performance evaluation.

### SIMS 1634 Statistics for Business and Behavioral Sciences I

Descriptive Statistics, exploratory data analysis, correlation, least square lines, probability, Random variables, normal distribution, sampling distributions, estimation and confident intervals, elementary hypothesis testing, one way analysis of variance using non-parametric and parametric tests.

### SIMS 1643 Statistics for Business and Behavioral Sciences II

Binomial distribution and normal approximation to the binomial, hypothesis testing and non-parametric inference for one and two populations, goodness of fit and contingency tables, one way analysis of variance and multiple comparism, block designs, Friedman test, further topic in regression.

### SIMS 2513 Calculus of Several Variables

The course treats functions of several variables, partial differentiation and applications, vectors in R2 and R3, multiple and iterated integrals, polar coordinates, spherical and cylindrical coordinates and multiple integrals. Change of variable in multiple integrals.

### SIMS 3513 Vector Functions and Differential Equations

Vector functions and their derivatives. Line integrals, Infinite series. Differential equations: first and second-order linear equations and application; series solutions.

### SIMS 3523 Ordinary Differential Equations

Topics include Laplace transforms and applications, systems of linear differential equations, Bessel and gamma functions. Sturm-Liouville problems, orthogonal functions, Fourier series. Prereq: SIMS 3513.

### SIMS 3533 Introduction Probability and Statistics

General introduction to the nature of statistics, method of data reduction, descriptive statistical analysis of frequency data, calculation of measure of central tendency and dispersion, moments, skewness and Kurtosis. Elements of combinatorial analysis. Relative frequency interpretation of probability, laws of probability, mutually exclusive and exhaustive events, conditional probability and statistical independence.

### SIMS 4523 Advanced Mathematical Modeling

Aspects of mathematical modeling, dimensional analysis, multiple scale analysis, asymptotic methods, differencial equations, calculus of variations.

### SIMS 4543 Cryptography

The course introduces students to modern cryptographic techniques and their mathematical foundations. Review of elementary number theory and algebra; classical cryptosystems; encryption standards; public key cryptosystems; e-Business applications; digital signatures. Elliptic curve cryptography and quantum cryptography may be included.