Credit Hours - 3

This course is in two parts. The first part is an introduction to programming using the python programming language. This part of the course begins with the basics of python. Vectorization, and visualization in python are also treated. The second part is an introduction to solving mathematical problems numerically. These problems include

finding the roots of nonlinear equations, solving large systems of linear equations and fitting polynomials to data. By the end of this course, students will be able to use python to solve basic mathematical problems.

Reading List:

• Burden, R.L. & Faires, J. D. (2008). Numerical analysis (9th Edition). Cengage Learning. 
• Chapra, S. (2008). Applied numerical methods with Matlab for engineers and scientists (3rd Edition). McGraw Hill.
• Langtangen, H.P. (2016). A primer on scientific programming with python (2nd Edition) Springer.             
• Lott, S.F. (2015). BuildingSkills in Python, Release 2.6 {\url{http://buildingskills.itmaybeahack.com/book/python2.6/latex/BuildingSkillsinPython.pdf}},
• Varoquaux, G., Gouillart, E. & Olaf, V.  (2015).  Scipy lecture notes, \url{www.scipy-lectures.org}
• Wiki (2015). Non-Programmer's Tutorial for Python 2.6, \url{https://upload.wikimedia.org/wikipedia/commons/6/69/Non-Programmer%27s_Tutorial_for_Python_2.6.pdf}

Credit Hours - 3

This is the first course in abstract algebra and as such it will be the students’ first approach to an axiomatic presentation of Mathematics. Among the topics to be discussed are notions of relations on sets, equivalence relations and equivalence classes as well as the concept of partial ordering. The system of real numbers and their properties will be discussed. The principle of induction will be reviewed.  An introduction to number theory will be given as numbers are the most familiar mathematical objects. The course seeks also to introduce axiomatically defined systems like groups, rings and fields, and vector spaces.  

Reading List:

• Fraleign, J. B (2013). A First Course in Abstract Algebra (8th Edition). Addison Wesley. 
• Friedberg, S.H., Insel, A.J., & Spence, L.E (2012). Linear Algebra (2nd Edition). Prentice-  Hall. 
• Goodaire, E.G. & Parmenter, M.M. (2006). Discrete Mathematics with Graph Theory (3rd Edition). Pearson Prentice Hall.
• Herstein, I.N. (2012). Abstract Algebra, 2nd edition, Macmillan.
• Rotman, J.J. (2006). A First Course in Abstract Algebra with Applications (3rd Edition). Pearson Prentice Hall.

Credit Hours - 3

Vector functions of a scalar variable; further differentiation and integration; Serret-Frenet formulae; differential equations of a vector function. Motion of a particle; Kinematics, Newton's laws; concept of a force; work, energy and power; impulse and momentum, conservation laws of energy and linear momentum. Rectilinear motion, motion in a plane. Two-body problem, variable mass.

Reading List:

• Bostock, L. & Chandler, S. (2012). Further Mechanics and Probability. Stanley Thomas Ltd, Wellington Street, England.
• Bostock, L. & Chandler, S. (2014).  Modular Mechanics, Module F, Mechanics 2. Stanley Thornes (Publishers) Ltd, Wellington Street, England.
• Bostock, L. & Chandler, S. (1989). Mathematics Mechanics and Probability. Stanley Thornes (Publishers) Ltd, Wellington Street, England.
• Spiegel, M. R. (2015).  Schaum's Outline of Theory and Problems of  Theoretical Mechanics. SI (Metric) Edition, McGraw-Hill Book Company, Singapore. 
• Tranter, C. J. & Lambe, C. G. (2010). Advanced Level Mathematics (Pure and Applied), 
• (4th Edition). Hodder Headline PLC, London Sydney Auckland, Toronto.

Credit Hours - 3

This is a first course in the applications of differentiation and integration of vector functions of a scalar variable. Kinematics of a single particle in motion, displacement, velocity acceleration. Relative motion. Concept of a force, line of action of a force, Newtons laws of motion. Motion in a straight line, motion in a plane, projectiles, circular motion. Work, energy, power. Impulse and linear momentum. Moment of a force, couple, conditions for equilibrium of rigid bodies.

Reading List:

• Bostock, L. & Chandler, S. (2012). Mathematics Mechanics and Probability. Stanley Thornes (Publishers) Ltd, Wellington Street, England.
• Hebborn, J. & Littlewood, J. (2014). Heinemann Modular Mathematics for London AS and A-level Mechanics 2. Heinemann Educational Publishers, Halley Court, Jordan Hill, Oxford.
• Jefferson, B. & Beadsworth, T. (2012). Introducing Mechanics. Oxford University Press. 
• Solomon, R.C. (1997). A Level Mechanics (4th Edition). Hillman Printers (Frome) Ltd, Great Britain.
• Tranter, C. J.  and Lambe, C. G. (2014)  Advanced Level Mathematics (Pure and Applied), (4th Edition). Hodder Headline PLC, London Sydney Auckland.

Credit Hours - 3

The first and the second derivatives of functions of  a single variable and their applications. Integration as a sum; definite and indefinite integrals; improper integrals. The logarithmic and exponential functions, the hyperbolic functions and their inverses. Techniques of integration including integration by parts, recurrence relations among integrals, applications of integral calculus to curves: arc length, area of surface of revolution. Ordinary differential equations: first order and second order linear equations with constants coefficients. Applications of first order differentials equations.

Reading List:

• Ayres, F. Jr. & Mendelson, E. (2009). Schaum's Outline Series Theory and Problems Differential and Integral Calculus. McGraw-Hill Book Company, New York. 
•  Backhouse, J.K., Houldsworth S.P.T., & Cooper, B.E.D. (2012). Pure Mathematics, A Second Course SI Edition, Oxford.
• Edwards, C.H.Jr. & Penney, D.E. (2012). Calculus and Analytic Geometry (6th Edition).Pearson.
• Larson, R.E., Edwards, B. H.  & Hostetler, R.P. (2014). Calculus of a Single Variable,Early transcendental functions(6th Edition). Cengage Learning.
• Stewart, J. (2016). Calculus (8th Edition).  Cengage Learning. 
• Tranter, C.J., & Lambe, C.G. (2012). Advanced Level Mathematics (Pure and Applied),            (4th Edition). Hodder Arnold H&S.