Undergraduate Courses

The Department of Mathematics offers the following programmes:

  • Single Major in Mathematics
  • Major-Minor in Mathematics
  • Combined-Major in Mathematics

The Department runs Single Major (3:2:1:1), Major-Minor (3:2:2:1) and Combined (3:2:2:2) programmes in Mathematics

Single Major in Mathematics
To be considered for the single major programme in Mathematics, students should have passed MATH 121, 122, 123 and 126 at 100 level.

Major – Minor in Mathematics
To be considered for the major-minor programme in Mathematics, students should have passed MATH 121, 122, 123 and 126 at 100 level.

Combined Major
To be considered for the combined major programme in Mathematics, students should have passed MATH 121, 122, 123 and 126 at 100 level.

 

For more details visit the student handbook.

Course Code Title
MATH 460 Fourier Series and Fourier Transfroms

Credit Hours - 3

The objective of this course is to introduce the theory of Fourier series and Fourier transforms on the real line.  Topics include: convolutions, summability kernels, convergence of Cesaro means. Mean-square convergence, pointwise convergence.

Fourier transform on the real line, inversion formula, Plancherel formula, Weierstrass approximation theorem. Applications to partial differential equations, Poisson summation formula. The Heisenberg uncertainty principle.

Reading List:

  • Katznelson, Y. (2002). An introduction to harmonic analysis, available at www.mat.uniroma2.it/~picard/SMC/..../Katznelson/Katznelson.pdf
  • Pinkus, A. & Zafrany, S. (1997). Fourier Series and Integral Transforms. Cambridge.
  • Sneddon I. N. (2010). Fourier Transforms. Dover Books on Mathematics
  • Stein, E.M., & Shakarchi, R. (2013). Fourier analysis, an introduction. Princeton.
  • Weaver, H. J. (1989). Theory of discrete and continuous Fourier analysis.   JohnWiley and Sons, NewYork.
MATH 458 Mathematical Biology II

Credit Hours - 3

The detail of this course may be informed by the student choice(s) of project topic and could include: (i) modelling of biological systems using partial differential equations. Derivation of conservation equations. Different models for movement. Connection between diffusion and probability.

(ii) Linear reaction-diffusion equations and fundamental solutions. Speed of a wave of invasion. Non-linear reaction-diffusion equations. Travelling wave solutions for monostable equations and bistable equations.

(iii) Systems of reaction-diffusion equations and travelling wave solutions. Pattern formations. Pattern formations in chemotaxis equations. (iv) Mathematical modelling of infectious diseases

Derivation of a simple SIR model and travelling wave solutions.

Reading List:

  • Britton, N. F. (2003). Essential Mathematical Biology. Springer.
  • De Vries,  G.,  Hillen, T.,   Lewis, M.,  Muller, J., & Schonfisch, B. (2006). A Course in Mathematical Biology. Quantitative Modeling SIAM.
  • Edelstein-Keshet, L. (1987). Mathematical Biology I, An introduction. Springer.
  • Segel, L.A., & Edelstein-Keshet, (2013).  A primer on mathematical models in biology. SIAM.
  • Murray, J.D. (2007). Mathematical Biology I, An introduction. Springer
MATH 452 Introduction to Lie Group and Lie Algebra

Credit Hours - 3

This course will cover the basic theory of Lie groups and Lie algebras. Topics may include: topological groups and Haar measure, vector fields and groups of linear transformations. The exponential map. Linear groups and their Lie algebras. Structure of semi-simple Lie algebras, Cartan and Iwasawa decompositions. Connectedness. Closed subgroups. The classical groups. Manifolds, homogeneous spaces and Lie groups. Integration and representations.
 

Reading List:

  • Carter, R., Segal, G., & Macdonald, I. (1995). Lectures on Lie Groups and Lie Algebras. Cambridge
  • Hall, B. (2009). Lie groups, Lie algebras and Representations-an elementary introduction. Springer
  • Krillov, A. (2006 ). An introduction to Lie groups and Lie algebras Cambridge. University Press
  • Sagel, A. A., & Walde, R. E. (2013). An introduction to Lie groups and Lie algebras.  Academic Press Inc.
  • Serre, J. P. (2005). Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University. Springer
MATH 448 Special Relativity

Credit Hours - 3

By employing the mathematics of sets, mappings and relations, we aim to develop an ability to think relativistically, exploring the relationship between space and time. Topics include: Galilean relativity, postulates of special relativity; Lorentz transformations. Lorentz-Fitzgerald contraction, time dilation. 4-vectors, relativistic mechanics, kinematics and force, conservation laws; decay of particles; collision problems, covariant formulation of electrodynamics.

Reading List:

  • Dray, T. (2012).  The geometry of special relativity. CRC Press
  • Frankel, T. (2013). The Geometry of Physics (3rd Edition). Cambridge
  • Matsko, V. J., & Noll, W. (1993).  Mathematical Structures of Special Relativity. available at http://repository.cmu.edu/cgi/viewcontent.cgi Article=1014&content=math
  • Susskind, L., & Friedman, A. (2017). Special Relativity and Classical Field Theory: The Theoretical Minimum. Basic Books.
  • Woodhouse, N. M. J. (2003). Special Relativity. Springer Undergraduate Mathematics Series
MATH 446 Module Theory

Credit Hours - 3

In this course we shall study the mathematical objects called modules. The use of modules was pioneered by one of the most prominent mathematicians, Emmy Noether (a German), who led the way in demonstrating the power and elegant of this structure. Topics include: modules, submodules, homomorphism of modules. Quotient modules, free (finitely generated) modules. Exact sequences of modules. Direct sum and product of modules.Chain conditions, Noetherian and Artinian modules. Projective and injective modules. Tensor product, categories and functors. Hom and duality of modules. 

Reading List:

  • Blyth, T. S. (2015).  Module theory; an approach to linear algebra. Oxford University Press
  • Dummit, D. S., & Foote, R. M. (2003). Abstract Algebra (3rd Edition). Wiley.
  • Lam, T.Y. (1998). Lectures on Modules and Rings. Springer GTM.
  • Rotman, J. (2008). An Introdution to Homological Algebra (2nd Edition). Springer Universitext
  • Wisbauer, R. (2011). Foundations of Module and Ring Theory. Available at ht
MATH 444 Calculus on Manifolds

Credit Hours - 3

This course aims to provide an introduction to Differentiable Manifolds and the tools for performing calculus on these objects; tangent vectors and differential forms. We will see how concepts like the derivative in Rn is extended to a smooth n-dimensional manifold. Topics include: manifold, submanifold, differentiability of maps between manifolds, the tangent space, the tangent bundle and the tangent functor. Vector bundle. The exterior algebra, the notion of a differentiable form on a manifold, singular n-chains and integration of a form over a chain. Partition of unity. Application to Stokes' theorem.

Reading List:

  • Jones, A., Gray, A., & Hutton, R. (1987).  Manifolds and Mechanics Aust. Math Soc. Lecture series (2), Cambridge University Press.
  • Lee, J. M. (2012). Introdution to Smooth Manifolds. Springer GTM
  • Spivak, M. (2015).  Calculus on Manifolds. Addison-Wesley
  • Spivak, M. (1999). A Comprehensive Introduction to Differential Geometry (3rd Edition). Vol 1, , Publish or Perish
  • Tu, L.W.  (2011). An Introduction to Manifolds. Universitext
MATH 442 Integration Theory and Measure

Credit Hours - 3

Algebra of sets, measurable sets and functions, measures and their construction (in particular Lebesgue measure), measure spaces. Integration, convergence theorems (Fatou’s Lemma, Monotone Convergence Theorem, Lebesgue Dominated Convergence Theorem). Lebesgue spaces, elementary inequalities, modes of convergence. Product measures and Fubini’s theorem.
Generalisation of the Riemann (R) integral (eg Kurzweil-Henstock (KH) integral). Lebesgue (L) integral. Relationship between the KH-integrable, L-integrable and R-integrable functions.   

Reading List:

  • Bass, R. Real Analysis for Graduate Students, (3rd Edition).
  • Cannarsa, P. & D'Aprile, T. D. (2007). Lecture notes on measure and functional analysis. https://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf     
  • Rudin, W. (1966). Real and ComplexAnalysis available  at             http://ruangbacafmipa.staff.ub.ac.id/files/2012/02/Real-and-Complex-Analysis-by-Walter Rudin.pdf
  • Stein, E., & Shakarchi, R. (2005). Real analysis:measure theory, integration and Hilbert spaces Princeton Lectures in Analysis.
  • Yee, L. P. & Vyborny, R. (2000). The integral: an easy approach after Kurzweil and Henstock. Aust Math Soc Lecture series 14. Cambridge University Press
MATH 449 Electromagnetic Theory II

Credit Hours - 3

This is a second course in the development of the mathematical foundations for the application of the electromagnetic model to various problems. Magnetostatics: steady currents, heating affect and magnetic field, magnetic vector potential, magnetic properties of matter, dipoles, induced magnetism, permanent magnetism. Time-varying fields: electromagnetic induction. Differential form of Faraday’s law, energy in electromagnetic fields. Maxwell’s equations and their consequences Poynting vector; electromagnetic potentials formation of electrodynamics.

Reading List:

  • Chirgwin, B. H., Plumpton, C., & Kilmister, C.W. (1972).  Elementary Electromagnetic Theory. Vols. II.  and III.     Pergamon Press.           
  • Fleisch, D. (2008). A Student's guide to Electromagnetic Theory. Cambridge.
  • Griffiths, D.J. (2014). Introduction to Electrodynamics. Pearson Educational
  • Jackson, J.D. (1962). Classical Electrodynamics. Wiley and Sons
  • Reitz, J. R., Milford. F. J., & Christy, R.W. (1979). Foundations of Electromagnetic Theory (3rd  Edition). Narosa Pub. House

     
MATH 457 Mathematical Biology I

Credit Hours - 3

In this course we focus on 3 types of biological phenomena to be modelled, namely single species population dynamics, interacting species and molecular dynamics. In single species population dynamics we will use difference equations: graphical analysis, fixed points and linear stability analysis. First order systems of ordinary differential equations: logistic equation, steady states, linearisation, and stability. And we will examine applications to 

harvesting and fisheries. For interacting species we examine systems of difference equations (host-parasitoid systems)and systems of ordinary differential equation (predator-prey and competition models) Finally, we will consider biochemical kinetics: Michaelis-Menten kinetics and metabolic pathways: activation and inhibition.

Reading List:

  • Britton, N. F. (2003). Essential Mathematical Biology. Springer.
  • De Vries, G., Hillen, T., Lewis, M.,  Muller, J., & Schonfisch, B. (2006) A Course in Mathematical Biology. Quantitative Modeling SIAM.
  • Edelstein-Keshet,  L. (1987). Mathematical Models in Biology. Birkhauser.
  • Murray, J. D. (2007). Mathematical Biology I, An Introduction. Springer.
  • Segel, L.A., & Edelstein-Keshet, (2013).  A primer on mathematical models in biology. SIAM.
MATH 445 Introductory Function Analysis

Credit Hours - 3

This course aims to use the methods of mathematical analysis and apply them to a special kind of vector space – Function spaces. The course begins with finite dimensional normed vector spaces and treats the following topics: Equivalent norms. Banach spaces. Infinite-dimensional normed vector spaces--Hamel and Schauder bases; separability. Compact linear operators on a Banach space. Complementary subspaces and the open-mapping theorem. Closed Graph theorem. Hilbert spaces. Special subspaces of and and the dual space. The completion of a normed vector space. Reflexive Banach spaces 

Reading List.

  • Eidelman, Y., Milman, V., & Tsolomitis, A. (2004). Functional Analysis: An Introduction. AMS
  • Kreyszig, E. (2013).  Introductory Functional Analysis. Wiley and Sons
  • Lax, P. (2004). Functional Analysis. Wiley-Interscience.
  • Rudin, W. (1966). Real and ComplexAnalysis available  at             http://ruangbacafmipa.staff.ub.ac.id/files/2012/02/Real-and-Complex-Analysis-by-Walter Rudin.pdf
  • Royden, H. (1988).  Real analysis. Prentice Hall
MATH 455 Computational Mathematics II

Credit Hours - 3

This course looks at methods of discretizing and solving differential equations. It begins with the solution of initial value problems for ordinary differential equations. We start with the Euler methods and systematically develop high order solutions for solving problems. The course then develops the concept of finite differences to solve boundary value problems.  In addition, we look at the problem of discretizing partial differential equations in space and time both implicitly and explicitly.

Reading List:

  • Burden, R. L., &  Faires, J. D. (2008). Numerical analysis. Cengage Learning (9th Edition).
  • Chapra, S. (2008). Applied numerical methods with Matlab for engineers and scientists  (3rd Edition). McGraw Hill.
  • Epperson, J. F. (2013). An introduction to numerical methods and analysis (2nd Edition). Wiley.
  • Gautschi, W. (2012). Numerical Analysis (2nd Edition). Birkhauser.
  • Matthews, J.H., & Fink, K.D. (2014). Numerical methods using Matlab (5th Edition). Pearson. 
  • Sauer, T. (2006).  Numerical Analysis. Pearson.
MATH 453 Introduction to Quantum Machanics

Credit Hours - 3

This course introduces students to the equations govening extremely small particles and their interactions. It introduces new mathematics to model the behavior of such objects. Topics include: The principle of least action, Hamilton's equation, Poisson brackets. Liouville's equation. Canonical transformations. Symmetry and conservation laws. Postulates of quantum mechanics, the wave formalism. Dynamical variables. The Schrodinger equation in one-dimension; free particles in a box, single step and square well potentials. Orbital angular momentum. The 3-dimensional Schrodinger equation; motion in a central force field, the 3-d square well potential, the hydrogenic atom. Heisenberg's equation of motion, harmonic oscillator and angular momentum. 

Reading List:

  • Jackson, J. D., (2006).  Mathematics for quantum mechanics- Dover Publications 
  • von Neumann, (1955), The Mathematical Foundations of Quantum Mechanics. Princeton Landmarks in Mathematics.
  • Shankar, R., (2011). Principles of quantum mechanics. Plenum Press
    Susskind, L., & Friedman, A. (2012). Quantum Mechanics- the theoretical minimum. Basic Books.
  • Woit, P. (2016).  Quantum Theory, Groups and Representations:  An Introduction available at http://www.math.columbia.edu/~woit/QM/qmbook.pdf
MATH 451 Introduction to Algebraic Field Theory

Credit Hours - 3

The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these problems are impossible.

This course aims to introduce students to the idea of a field in algebra, and investigates properties of algebraic fields, of finite and zero characteristic.

Reading List:

  • Eisenbud, D. (1999). Commutative Algebra with a view towards Algebraic Geometry. Springer GTM.
  • Fraleigh, J. B. (2013). A First Course in Abstract Algebra (8thEdition). Addison Wesley.
  • Gallian, J. A. (2013).  Contemporary Abstract Algebra (8th Edition). Brooks/Cole
  • Jones, A., Morris, S., & Pearson, K.R. (1991). Abstract algebra and famous impossibilities. Universitext, Springer.
  • Rotman, J. (2006). A First Course in Abstract Algebra with Applications (3rd Edition). Pearson
MATH 443 Diffrential Geometry

Credit Hours - 3

The modern approach to differential geometry uses the language of manifolds. This provides a theory and a variable free notation which frees us from always having to consider the coordinate system. We want to be able to deal with the elements of calculus both invariantly (i.e. independently of the local coordinates) and intrinsically (i.e. independently of the way a geometric object is embedded in Euclidean space). But to appreciate the great contribution to differential geometry made by the theory of manifolds, we will first study classical differential geometry and then a little of the modern approach.

Reading List: 

  • Carmo, M. (2016). Differential Geometry of Curves and Surfaces (2nd Edition). Dover. 
  • Kuhnel, W. (2006). Differential Geometry -Curves SurfacesManifolds. AMS.
  • Millman, R. S., & Parker, G. D. (2007). Elements of Differential Geometry. Pearson
  • O'Neill, B. (2012). Elementary Differential Geometry. Academic Press
  • Willmore, T. J. (2007). Introduction to Differential Geometry. Oxford University Press
MATH 440 Abstract Algebra II

Credit Hours - 3

This is a second course in group theory Topics covered will include: finite groups, Sylow theorems and simple groups. Composition series. We state and prove the Zassenhaus Lemma, the Schreier theorem and the Jordan-Hölder theorem. Direct and semi-direct products. Abelian groups, torsion, torsion-free and mixed abelian groups. Finitely generated group and subgroups. P-groups, nilpotent groups and solvable groups. 

Reading List:

  • Dummit, D. S. & Foote, R. M. (2003). Abstract Algebra (3rd Edition). Wiley
  • Fraleign, J. B. (2013). A First Course in Abstract Algebra (8th Edition). Addison Wesley.
  • Gallian, J. A. (2013).  Contemporary Abstract Algebra (8th Edition). Brooks/Cole
  • Judson, T. (2015). Abstract Algebra: Theory and Applications. Open Source available http://abstract.ups.edu/index.html 
  • Pinter, C. C. (2010).  A Book of Abstract Algebra (2nd Edition). (Dover Books on Mathematics)
MATH 447 Complex Analysis

Credit Hours - 3

The objective of this course is to introduce students to complex numbers and functions of a complex variable. We introduce the notions of differentiability (and analyticity) and integrability for a function defined on the complex plane. We also look at ways in which one can integrate complex-valued functions. Elementary topology of the complex plane. Complex functions and mappings. The derivative. Differentiability and analyticity. Harmonic functions. Integrals. Maximum modulus, Cauchy-Gorsat, Cauchy theorems. Applications. Taylor and Laurent series, zeros and poles of a complex function. Residue theorem and consequences. Conformal mapping, analytic continuation.

Reading List:

  • Alfors, L.V. (1979). Complex Analysis. McGraw-Hill.
  • Saff, E. B. & Snider, A. B. (2013). Fundamentals of Complex Analysis. Pearson Educational
  • Stewart, I. N., & Tall, D.O. (2011). Complex Analysis. Cambridge University Press.
  • Wunsch, A.D. (2005). Complex Variables with Applications. Pearson Educational
  • Zill, D. G., & Shanaban, (2003). A First Course in Complex Analysis. Jones and Bartlett
MATH 441 Advanced Calculus

Credit Hours - 3

Here we think of differentiation as a process of approximating the function near a, by a linear map. This linear map is called the Fr ́echet derivative of at a. The main aim of this course is to understand two of the most important theorems for modern analysis: the

Inverse Map Theorem and the Implicit Function Theorem. Other ideas include:

linear and affine maps between normed vector spaces. Limits, continuity, tangency of maps and the derivative as a linear map. Component-wise differentiation, partial derivatives, the Jacobian as the matrix of the linear map. Generalized mean value theorem. 

Reading List:

MATH 368 Introductory Number Theory

Credit Hours - 3

This course builds on the elementary number theory introduced in MATH 224 Topics include: the Fundamental theorem of Arithmetic, Proof and Application: GCD,

LCM. Asymptotic notations,Congruences: Introduction to Congruences, Residue systems and Euler Phi-function, Linear Congruence, Chinese Remainder theorem, Theorems of Euler, Fermat and Wilson Arithmetic functions and Dirichlet Multiplication: Mobius, Euler Phi, Mangoldt, Sum of divisors etc functions, Dirichlet’s product and Mobius inversion formula, averages of arithmetical functions Quadratic Residues and Quadratic Reciprocity Law: Quadratic Residues, Legendre’s symbol and its properties, The quadratic reciprocity law and applications, the Jacobi symbol. Prime Number distribution.

Reading List:

  • Apostol, T. M. (1998). Introduction to Analytical number theory.  Springer
  • Chandrasekharan, K. (2012).  Introduction to Analytical number theory. Springer
  • Tenenbaum, G(2015). Introduction to Analytical and Probabalistic number theory. Springer.
  • Jones, G., & Jones, J. (1998). Elementary Number Theory. Springer
  • Ireland, K., & Rosen, M. (1998). A Classical Introduction to Modern Number Theory (2nd Edition). Springer
MATH 358 Computational Mathematics I

Credit Hours - 3

This course is a sequel to Math220. In this course, we continue the solution of linear systems by treating matrices with special structures. We also continue with data fitting using polynomials. Several high order methods for discretizing the derivative and definite integral are also treated. The course ends with approximations of eigenvalues for large matrices. We explain the concept of the dominant eigenvalue and its eigenvector. We also look at simultaneous approximation of eigenvalues.

Reading List:

  • Burden, R. L. & Faires, J. D. (2008). Numerical analysis. Cengage Learning, (9th Edition).
  • Chapra, S. (2008). Applied numerical methods with Matlab for engineers and scientists (3rd Edition). McGraw Hill.
  • Epperson, J. F. (2013). An introduction to numerical methods and analysis (2nd Edition).Wiley.
  • Matthews, J.H. & Fink, K.D. (2014). Numerical methods using Matlab. Pearson (5th Edition).
  • Sauer, T. (2006).  Numerical Analysis. Pearson.
MATH 372 Topology

Credit Hours - 3

This is a first course in point set topology. Students will be introduced to 
topological spaces and be able to identify open and closed sets with respect to the given topology. Other aspects to be discussed are basis for a topological space. Separation and countability properties. Limit points. Connectedness. Subspace topology. Homeomorphism.Continuity. Metrizability. Continuity via convergent sequences. Compactness. 

Reading List:

  • Davis, S. W. (2004 ). Topology. McGraw-Hill Higher Education.
  • Lipschultz, S. (1965). Schaum's outline of theory and problems of general topology. Schaums Outlines.
  • McIntyre, M. (2009). Topology. Departmental Lecture Notes
  • Chirgwin, B.H, Plumpton, C., & Kilmister, C.W. (1972).  Elementary Electromagnetic Theory. Vols. II.  and III.     Pergamon Press.      
  • Griffiths, D.J. (2014). Introduction to Electrodynamics. Pearson Educational
  • Jackson, J. D. (1962). Classical Electrodynamics. Wiley and Sons.
  • Reitz, J.R., Milford. F. J., & Christy, R.W. (1979). Foundations of Electromagnetic Theory (3rd  Edition). Narosa Pub. House.
  • Morris, S. (2011). Topology. without tears ebook.
MATH 356 Analysis II

Credit Hours - 3

This is a continuation of MATH 353. We now consider vector spaces of functions and discuss convergence of sequences of functions; pointwise and uniform convergence. Other topics discussed include; power series, the contraction mapping theorem and applications. We examine the definition of  the Riemann integral and conditions for integrability. We give a proof of the fundamental theorem of calculus and major
basic results involved in its proof . We finish with some point set topology in R.

Reading List:

  • Davidson, K. R. & Donsig, A. P. (2010). Real Analyis and its Applications. Springer
  • Lang, S. (2015). Undergraduate Analysis. Springer
  • McIntyre, M. (2016). Analysis notes. Departmental Lecture Notes.
  • Royden, H. & Fitzpatrick, P. (2010). Real Analysis (4th Edition).
  • http://math.harvard.edu/~ctm/home/text/books/royden-fitzpatrick/royden-fitzpatrick.pdf
  • Rudin, W. (1976). Principles of Mathematical Analysis. McGraw-Hill Higher Education.
MATH 354 Abstract Algebra I

Credit Hours - 3

The primary aim of Math 354 is to study groups and their properties. We shall develop the foundations of group theory and study some notable groups like cyclic groups, permutation groups, finite Abelian groups and their characterization. Other ideas include: subgroups, cyclic groups.The Stabilizer-Orbit theorem.Lagrange's theorem. Classifying groups. Structural properties of a group. Cayley's theorem. Generating sets. Direct products. Finite abelian groups. Cosets and the proof of Lagrange's theorem. Proof of the Stabilizer-Orbit theorem. 

Reading List:

  • Dummit, D. S. & Foote, R. M. (2003). Abstract Algebra (3rd Edition). Wiley
  • Fraleign, J. B. (2013). A First Course in Abstract Algebra (8th Edition). Addison Wesley.
  • Gallian, J. A. (2013).  Contemporary Abstract Algebra (8th Edition). Brooks/Cole.
  • Judson, T. (2015). Abstract Algebra: Theory and Applications. Open Source available at
  • http://abstract.ups.edu/index.html 
  • Pinter, C. C. (2010).  A Book of Abstract Algebra (2nd Edition). (Dover Books on Mathematics).
MATH 363 Introductory Concepts of Financial Mathematics

Credit Hours - 3

This course introduces the basic methods applied in financial mathematics. We will discuss probability functions, stochastic processes, random walks and martingales; Ito's lemma and stochastic calculus. Students will understand the stochastic differential equations for a geometric Brownian motion process. We will study mean reverting models such as the Ornstein- Uhlembeck process, as well as stochastic volatility models such as the Heston Model. Stochastic models for stock pricing are also discussed;  we study a binomial option pricing model, the Black-Scholes model and the capital asset pricing model.

Reading List:

  • Bass, R. (2003). The basics of financial mathematics. Springer.
  • Doob, J. L. (2014). Stochastic processes. Wiley Interscience.
  • Wilmott, P. & Howison, S. (1995). The Mathematics of Financial Derivatives: A Student    Introduction. Cambridge University Press.
  • Oksendal, B. (2010). Stochastic Differential Equations (5th Edition). Universitext
  • Parzen, E. (2010). Modern probability theory and applications. John Wiley, Canada
MATH 361 Classical Mechanics

Credit Hours - 3

The methods of classical mechanics have evolved into a broad theory of dynamical systems and therefore there are many applications outside of Physics; for example to biological systems.  Topics to be discusses will include1-dimensional dynamics: damped and forced oscillations. Motion in a plane: projectiles, circular motion, use of polar coordinates and intrinsic coordinates. Two-body problems, variable mass. Motion under a central, non-inertial frame. Dynamics of a system of particles. 

Reading List:

  • Corben, H. & Stehle, P. (1994). Classical Mechanics (2nd edition). Dover
  • Kibble, T. W. B. & Berkshire, F. H. (2011). Classical mechanics (5th Edition). Imperial College Press.
  • Marsden, J. & Abraham, R. (2012). Foundations of mechanics. Westview Press.
  • Morin, D. (2008). Introduction to Classical Mechanics. Cambridge University Press. 
  • Susskind, L. (2014). Classical mechanics.  Penguin Books Ltd
MATH 359 Discrete MAthematics

Credit Hours - 3

This course is a study of discrete rather than continuous mathematical structures. Topics include: asymptotic analysis and analysis of algorithms, recurrence relations and equations, Counting techniques (examples include: Inclusion-exclusion and pigeon-hole

principles and applications, Multinomial Theorem, generating functions),

Elementary Number Theory and Cryptography, Graph Theory, Discrete probability

theory. Planarity, Euler circuits, shortest-path algorithm. Network flows. Modelling computation: languages and grammars, models, finite state machines, Turing machines 

Reading List:

  • Gossett, E. (2008). Discrete Mathematics with Proof.  Wiley.
  • Levin, O. (2013). Discrete Mathematics. http://discretetext.oscarlevin.com/home.php
  • Lipschultz, S. (2007). Schaum's outline of discrete mathematics. Schaums Outlines.
    Rajagopalan, S. P. & Sattanathan, R. (2015). Discrete mathematics. Margham Publications.
  • Rosen, K. H. (2012). Discrete mathematics and its applications. McGraw-Hill
MATH 362 Analytical Mechanics

Credit Hours - 3

In this course the student is introduced to  a collection of closely related alternative formulations of classical mechanics. It   provides a detailed introduction to the key analytical techniques of classical mechanics. Topics discussed include
rigid body motion, rotation about a fixed axis. General motion in a plane, rigid bodies in contact, impulse. General motion of a rigid body. Euler-Lagrange equations of motion.

Reading List:

  • Finch, J. D. & Hand, L.N. (1998). Analytical mechanics. Cambridge University Press
  • Fowles, G. R. & Cassiday, G. L. (2004). Analytical Mechanics (7th Edition). Brooks/Cole
  • Lanczos, C. (2011). The variational principles of mechanics. Dover
  • Merches, I. & Radu, D. (2014). Analytical Mechanics: Solutions to problems in Classical Physics. CRC press.
  • Helrich, C. (2017). Analytical Mechanics. Springer
MATH 366 Electromagnetic Theory I

Credit Hours - 3

This course develops the mathematical foundations for the application of the electromagnetic model to various problems. Mathematics discussed includes scalar and vector fields, grad, div and curl operators. Orthogonal curvilinear coordinates. Electrostatics: charge, Coulomb's law, the electric field and electrostatic potential, Gauss's law, Laplace's and Poisson's equations. Conductors in the electrostatic field. Potential theory.

  • Reading List:
  • Chirgwin, B.H., Plumpton, C., & Kilmister, C.W. (1972).  Elementary Electromagnetic Theory. Vols. II.  and III.     Pergamon Press.        
  • Friedriches, K. O. (2014). Mathematical Methods of Electromagnetic Theory. AMS 
  • Griffiths, D. J. (2014). Introduction to Electrodynamics. Pearson Educational.
  • Jackson, J. D. (1962). Classical Electrodynamics. Wiley and Sons
  • Reitz, J. R., Milford. F. J., & Christy, R.W. (1979). Foundations of Electromagnetic Theory, (3rd Edition). Narosa Pub. House. 
MATH 350 Diffrential Equations I

Credit Hours - 3

Differential equations can be studied analytically, numerically and qualitatively. The focus of this course is to find solutions to differential equations using analytic techniques. Differential forms of 2 and 3 variables. Exactness and integrability conditions. Existence and uniqueness of solution. Second order differential equations with variable coefficients. Reduction of order, variation of parameters. Series solution. Ordinary and regular singular points. Orthogonal sets of functions. Partial differential equations. 

Reading List:

  • Agarwal, R. P., &  O’Regan, D. (2009). Ordinary and Partial Differential Equations. Springer, New York.
  • Collatz, L. (2013).  Differential Equations : An Introduction and Applications. John Wiley and Sons Ltd.  
  • Edwards, C. H.,  & Penny, D. E. (2015). Elementary Differential Equations, (7th Edition). Pearson Education Ltd. 
  • Goodwine, B. (2011). Engineering Differential Equations - Theory and Applications. Springer, New York.
  • Zill, D. G. (2014). A first course in Differential Equations with Modelling Applications
  • (7th Edition). Brooks/Cole.
MATH 355 Calculus of Several Variables

Credit Hours - 3

The major goal for this course is to understand and apply the concepts of

differentiation and integration to functions of several variables.
Functions of several variables, partial derivative. Directional derivative, gradient. Local extema, constrained extrema. Lagrange multipliers. The gradient, divergence and curl operators. Line, surface and volume integrals. Green's theorem, divergence theorem, Stokes' theorem. 

Reading List

  • Lang, S. (2016). Calculus of Several Variables. Undergraduate Texts in Mathematics, Springer.
  • Marsden, J. & Tromba, A. (2003). Vector Calculus. W H Freeman.
  • Stewart, J. (2014). Multivariable Calculus (6th edition). Brooks/Cole
    Strang, G. ( 2012). Calculus(http://ocw.mit.edu/resources/res-18-001-calculus-online- textbook-spring-2005/textbook/).
  • Thomas, G. & Weir, M. (2013). Calculus: Early Transcendentals (13th Edition). Pearson
MATH 353 Analysis I

Credit Hours - 3

This is the first rigorous analysis course. Topics to be discussed include: normed vector spaces, limits and continuity of maps between normed vector spaces. Students will be expected to produce proofs to justify their claims.
We study the algebra of continuous functions. Bounded sets of real numbers. Limit of a sequence. Subsequences. Series with positive terms.Convergence tests. Absolute convergence. Alternating series. Cauchy sequences and complete spaces.

Reading List:

  • Davidson, K. R. & Donsig, A. P. (2010). Real Analyis and its Applications. Springer.
  • Lang, S. (2015). Undergraduate Analysis. Springer.
  • McIntyre, M (2016). Analysis notes. Departmental Lecture Notes.
  • Royden, H Fitzpatrick, P, (2016) Real Analysis, (4th edition). 
  • http://math.harvard.edu/~ctm/home/text/books/royden-fitzpatrick/royden- fitzpatrick.pdf
  • Rudin, W. (1976). Principles of Mathematical Analysis. McGraw-Hill Higher Education.
MATH 351 Linear Algebra

Credit Hours - 3

We will develop a core of material called linear algebra by introducing

definitions and procedures for determining properties and proving theorems about matrices and linear transformations, with applications. Topics to be discussed include: spanning sets; subspaces, solution spaces. Bases. Linear maps and their matrices. Inverse maps. Range space, rank and kernel. Eigenvalues and eigenvectors. Diagonalization of a linear operator. Change of basis. Diagonalizing matrices. Diagonalization theorem. Bases of eigenvectors. Symmetric maps, matrices and quadratic forms.

Reading List:

  • Hefferon, J. (2014).  Linear Algebra http://joshua.smcvt.edu/linearalgebra 
  • Kolman, B. (2003.) Linear Algebra (8th Edition).
  • Lang, S. (2014). Linear Algebra. Undergraduate Texts in Mathematics, Springer.
  • Lipshultz, S. (2008). Schaum’s outline of Linear Algebra. 
  • Robinson, D.J.S. (2012). A course in linear algebra with applications. World Scientific Publishing Co. Pty Ltd.
MATH 220 Introductory Computational Mathematics

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:

MATH 224 Introductory Abstract Algebra

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.
MATH 222 Vector Mechanics

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.
MATH 225 Vectors and Mechanics

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.
MATH 223 Calculus II

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.
MATH 126 Algebra and Geometry

Credit Hours - 3

This is a course which highlights the interplay of algebra and geometry.  It includes topics such as: polar coordinates; conic sections. Complex numbers, Argand diagram, DeMoivre's theorem, roots of unity. Algebra of matrices and determinants, linear transformations. Transformations of the complex plane.  Sketching polar curves and some coordinate geometry in 3 dimensions. Vector product and triple products. 

Reading List:

  • Beacher, J., Penna, J. A., &  Bittinger, M. L. (2005). College Algebra (2nd Edition). Addison Wesley
  • Copeland, A. H. (1962). Geometry, algebra and trigonometry by vector methods. Mac-Millan
  • Safler, F. (2012). Schaum's Outline of Precalculus (3rd Edition). McGraw-Hill Education
  • Spiegel, M.R., & Moyer, R.E. (2014).  Schaum's Outline of College Algebra (4th Edition). 
  • McGraw-Hill Education
MATH 122 Calculus I

Credit Hours - 3

Elementary idea of limit, continuity and derivative of a function. Rules of differentiation. Applications of differentiation. Derivative of the elementary and transcendental functions. Methods of integration. Improper integrals. Applications of integration. Formation of differential equations and solution of first order differential equations both separable variable type and using an integrating factor.

Reading List:

  • Hughes-Hallett, D., Gleason A.M., et al (1994).  Calculus. A. J. Wiley.
  • Kline, M. (1998). Calculus: An Intuitive and Physical Approach (2nd Edition). Dover.
  • Lang, S. (1998). A First Course in Calculus (Undergraduate texts). Springer.
  • Stewart, J. (1995). Calculus, concepts and context. Brooks/Cole 
  • Thomas, G.B., & Finney, R.L. (1995). Calculus and Analytic Geometry. Addison Wesley Publishing Company
MATH 123 Vectors and Geometry

Credit Hours - 3

Vectors may be used very neatly to prove several theorems of geometry. This course is about applying vector operations and the method of mathematical proof (of MATH 121) to geometric problems. The areas of study include: vector operations with geometric examples; components of a vector and the scalar product of vectors. Coordinate geometry in the plane including normal vector to a line, angle between intersecting lines, reflection in a line, angle bisectors and the equation of a circle, the tangent and the normal at a point.

Reading List:

  • Akyeampong, D.A., (2006). Vectors and Geometry. Departmental Lecture notes.
  • Backhouse, J.K., Houldsworth, S.P.T.,  & Horril, P.J.F. (2010). Pure Mathematics. Longman 
  • Bostock, L., Chandler. S., & Thorpes, S. (2014). Further Pure Mathematics. Oxford University Press.
  • Robinson, G. B. (2011). Vector geometry. Dover. 
  • Schuster, S. (2008). Elementary Vector Geometry. Dover.
MATH 121 Algebra and Trigonometry

Credit Hours - 3

This course is a precalculus course which aims to develop the students’ ability to think logically, use sound mathematical reasoning and understand the geometry in algebra. It includes advanced levels of topics addressed in high school such as arrangements, selections and the binomial theorem. Sequences and series. Logic and Proof.  Set theory. Indices, logarithms and the algebra of surds. Concept of a function. Trigonometric functions, their inverses, their graphs, circular measure and trigonometric identities. 

Reading List:

  • Backhouse, J.K., Houldsworth, S.P.T., & Cooper B.E.D. (2010). Pure Mathematics 2, Longman.
  • Bittinger, M. L. et al (2012) Algebra and Trigonometry (5th edition). Pearson
BCMB 111 Biochemistry

Credit Hours - 3

Carbohydrates Metabolism: Digestion of carbohydrates, glycolysis and fate of pyruvate in different organisms; tricarboxylic acid (TCA) cycle; pentose phosphate pathway and fate of reduced coenzymes; catabolism of monosaccharides other than glucose; gluconeogenesis, Calvin Benson cycle, Cori cycle, glyoxylate cycle; glycogenesis and glycogenolysis; regulation of carbohydrate metabolism; Diseases of carbohydrate metabolism. Aerobic metabolism of pyruvate, starvation and obesity. The coenzyme role of B vitamins. Changes in nutritional requirement and metabolic rate in injury and disease. Lipids Metabolism: Digestion of triacylglycerols; the different lipases (lipoprotein lipase, hormone-sensitive lipase); fate of glycerol; beta-oxidation of fatty acids; fate of products (acetyl and propionyl CoA, ketone bodies, reduced coenzymes); synthesis of fatty acids triacylglycerol, cholesterol; regulation of metabolism. Protein Metabolism: Digestion of proteins, transamination, deamination and decarboxylation of amino acids and the fate of ammonia (urea cycle) and carbon skeleton; metabolism of specific amino acids (aromatic and sulphur-containing amino acids); synthesis of amino acids; in-born errors of amino acid metabolism; regulation of metabolism. Enzymes as biological catalyst: Enzyme kinetics and concept of rate-determining step. Enzyme specificity and allosteric regulation. Mechanisms of enzyme action and examples. Coenzymes and vitamins. Drugs and their effect on enzymes.

BCMB 111 BIOCHEMISTRY

Credit Hours - 3

Carbohydrates Metabolism: Digestion of carbohydrates, glycolysis and fate of pyruvate in different organisms; tricarboxylic acid (TCA) cycle; pentose phosphate pathway and fate of reduced coenzymes; catabolism of monosaccharides other than glucose; gluconeogenesis, Calvin Benson cycle, Cori cycle, glyoxylate cycle; glycogenesis and glycogenolysis; regulation of carbohydrate metabolism; Diseases of carbohydrate metabolism. Aerobic metabolism of pyruvate, starvation and obesity. The coenzyme role of B vitamins. Changes in nutritional requirement and metabolic rate in injury and disease. Lipids Metabolism: Digestion of triacylglycerols; the different lipases (lipoprotein lipase, hormone-sensitive lipase); fate of glycerol; beta-oxidation of fatty acids; fate of products (acetyl and propionyl CoA, ketone bodies, reduced coenzymes); synthesis of fatty acids triacylglycerol, cholesterol; regulation of metabolism. Protein Metabolism: Digestion of proteins, transamination, deamination and decarboxylation of amino acids and the fate of ammonia (urea cycle) and carbon skeleton; metabolism of specific amino acids (aromatic and sulphur-containing amino acids); synthesis of amino acids; in-born errors of amino acid metabolism; regulation of metabolism. Enzymes as biological catalyst: Enzyme kinetics and concept of rate-determining step. Enzyme specificity and allosteric regulation. Mechanisms of enzyme action and examples. Coenzymes and vitamins. Drugs and their effect on enzymes.

BCMB 111 BIOCHEMISTRY

Credit Hours - 3

Carbohydrates Metabolism: Digestion of carbohydrates, glycolysis and fate of pyruvate in different organisms; tricarboxylic acid (TCA) cycle; pentose phosphate pathway and fate of reduced coenzymes; catabolism of monosaccharides other than glucose; gluconeogenesis, Calvin Benson cycle, Cori cycle, glyoxylate cycle; glycogenesis and glycogenolysis; regulation of carbohydrate metabolism; Diseases of carbohydrate metabolism. Aerobic metabolism of pyruvate, starvation and obesity. The coenzyme role of B vitamins. Changes in nutritional requirement and metabolic rate in injury and disease. Lipids Metabolism: Digestion of triacylglycerols; the different lipases (lipoprotein lipase, hormone-sensitive lipase); fate of glycerol; beta-oxidation of fatty acids; fate of products (acetyl and propionyl CoA, ketone bodies, reduced coenzymes); synthesis of fatty acids triacylglycerol, cholesterol; regulation of metabolism. Protein Metabolism: Digestion of proteins, transamination, deamination and decarboxylation of amino acids and the fate of ammonia (urea cycle) and carbon skeleton; metabolism of specific amino acids (aromatic and sulphur-containing amino acids); synthesis of amino acids; in-born errors of amino acid metabolism; regulation of metabolism. Enzymes as biological catalyst: Enzyme kinetics and concept of rate-determining step. Enzyme specificity and allosteric regulation. Mechanisms of enzyme action and examples. Coenzymes and vitamins. Drugs and their effect on enzymes.