Minor in Mathematics

Math Minor for Scientists and Engineers

The study of mathematics is crucial for the success of Science and Engineering students. Many topics in biology, chemistry, physics and engineering cannot be properly understood without a robust math background beyond the standard freshman Calculus I and II sequence.

The Minor in Mathematics comprises a central core of required courses followed by opportunities for advanced work and some specialization.

Impact on Current Degree Offerings

The Minor in Mathematics fits with the existing degrees offered at the Alfaisal University and it requires 26 Math credits beyond Pre-Calculus. This would be very attractive for Engineering students because they already have more than 20 Math credits required for the Engineering degree.

For our Science students, the additional math coursework may be heavy, but it could be attractive to those students interested and intent on learning mathematics, as well as for those hopping to become future researchers in their field.

Curriculum

The Math Minor curriculum consists:
  • • 17 credit hours of core courses: MAT 101: Calculus I (4 CHRs); MAT 112: Calculus II (4 CHRs); MAT 212: Linear Algebra (3 CHRs); MAT 213: (Ordinary) Differential Equations (3 CHRs); STA 212: Probability and Statistics (3 CHRs).
  • • 9 credit hours of elective courses to be selected from: MAT 211 (3 CHRs): Calculus III; MAT 224 (3 CHRs): Numerical Methods; MAT 320 (3 CHRs): Partial Differential Equations for Scientists & Engineers; MAT 321 (3 CHRs): Advanced Calculus; MAT 322 (3 CHRs): Complex Variables for Scientists & Engineers; MAT 420 (3 CHRs): Advanced Probability & Stochastic Process.

Math Minor Course Description

Core courses for Minor in Mathematics

MAT 101 - Calculus I (4 credits)

This course introduces the basic concepts of mathematical analysis used in science and engineering. The course teaches an introduction to differential and integral calculus. Topics include limits; the derivative; rates; Newton's method; the mean-value theorem; max-min problems; the integral and the fundamental theorem of integral calculus; areas, volumes, and average values.
Prerequisite: None.

MAT 112 - Calculus II (4 credits)

This course is a continuation to Calculus I. The course covers basic mathematical analysis and mathematical tools that are widely used and are essential for mathematical analysis and applications. Topics include sequences; infinite series; power series; conics; polar, cylindrical, and spherical coordinates; vectors and the geometry of space; and vector valued functions.
Prerequisite: MAT 101.

MAT 212 - Linear Algebra (3 credits)

The course teaches an introduction to linear algebra. Topics include complex numbers, geometric vectors in two and three dimensions and their linear transformations, the algebra of matrices, determinants, solutions of systems of equations, vector space, eigenvalues and eigenvectors.
Prerequisite: MAT 112.

MAT 213 Differential Equations (3 credits)

This course is an introduction to the theory and application of ordinary differential equations and the Laplace transform. The main objective is for the student to develop competency in the basic concepts and master certain solution methods. Topics covered include linear and nonlinear first order equations; higher order linear differential equations; undetermined coefficients method; variation of parameters method; Cauchy-Euler equation; Laplace transform; linear systems solution; solution by series method.
Prerequisite: MAT 112.

STA 212 - Probability and Statistics for Engineers (3 credits)

The course is designed to teach students the basics of probability and statistics as used in engineering and the sciences. The course covers introduction to probability theory, random variables, statistics, and regression.
Prerequisite: MAT 112.

Elective courses for Minor in Mathematics

MAT 211 - Calculus III (3 credits)

This course deals with multi-dimensional calculus. It is designed primarily for engineering majors and is taken by other technical majors. The student will develop an understanding of limits and continuity of functions of several variables; compute partial derivatives and apply to optimization problems; set up and compute iterated integrals to compute areas, volumes of solids; understand and apply Green's Theorem, the Divergence Theorem and Stoke's Theorem.
Prerequisite: MAT 112.

MAT 224 Numerical Methods (3 credits)

This course introduces the basic concepts of numerical analysis that are employed in science and engineering. It includes a solid introduction to the basic methods and approximation techniques in use, and to the reliability and accuracy of the approximations. Applications of the methods to simplified/model problems that represent real-life problems are also included. Programming skills (based on MATLAB) needed to implement the methods on a computer are also covered.
Prerequisite: MAT 212.

MAT 320 – Partial Differential Equations for Scientists and Engineers (3 credits)

This course deals with partial differential equations: first order equations (linear and nonlinear), heat equation, wave equation, and Laplace equation. Separation of variables. Method of characteristics for hyperbolic problems. Solution of initial boundary value problems using separation of variables and Eigen function expansions. Some numerical methods.
Prerequisite: MAT 212, MAT 213.

MAT 321 – Advanced Calculus (3 credits)

Detailed and analytical study of differential and integral calculus for types of functions of several variables; implicit function theorem, vector calculus; line, surface, and space integrals including Green's theorem, Divergence theorem, and Stokes' theorem.
Prerequisite: MAT 211, MAT 212.

MAT 322 – Complex Variables for Scientist and Engineers (3 credits)

This course is an introduction to complex variables accessible to juniors and seniors in engineering, physics and mathematics. The algebra of complex numbers, analytic functions, Cauchy Integral Formula, theory of residues and application to the evaluation of real integrals, conformal mapping and applications to physical problems.
Prerequisite: MAT 211.

MAT 420 – Advanced Probability and Stochastic Process (3 credits)

The objective of this course is to introduce the fundamental principle of probability measure theory and to introduce to stochastic processes. Large sample with a variety of convergence concepts and central limit theorems are included as first part. The second part is dedicated to stochastic processes that help students to model the complete evolution of the system related to telecommunication, Finance, Biology, and Physics. Topics will include branching processes, Random walk, Brownian motion, Markov processes, counting processes and discrete processes with the Markov property.
Prerequisite: MAT 112, STA 212.


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