Mathematics-with-Economics

Degree Type: 

Bachelor of Science

Department: 

Department of Mathematics

Programme Duration: 

4 years (Standard Entry)

Modes of Study: 

Regular

About Programme: 

In today’s increasingly complicated international business world, a strong preparation in the fundamentals of both economics and mathematics is crucial to success. Graduates can find work as economists, market research analysts, financial analysts, and financial planners, amongst several other rewarding career fields.

 

9 READING LIST 

                             

  1. Adams,  A. R. (2003). Calculus, A Complete Course, 6th Ed. Addison Wesley Longman.

  2. Ahlfors,  L. (1979).  Complex Analysis, McGraw-Hill.

  3. Allan, J. (2002). Advanced Engineering Mathematics, Harcourt/Academic Press, USA.

  4. Allen L, J.S. (2007). An Introduction to Mathematical Biology,  Pearson Education, New Jersey, USA

  5. Anderson, A. & May, R.  (1991). Infectious Diseases of Humans: Dynamics and Control,  Oxford University Press, London. United Kingdom.

  6. Anderson, D. R., Sweeney, D. J. & Williams, T. A. (1988). An Introduction to Management Science: Quantitative Approaches to Decision Making; 5 Ed., West Pub. Co., USA.

  7. Anton, H. & Rorres, C. (1988 ). Elementary Linear Algebra, Applications Version, John Wiley, New York, USA.

  8. Axler, S. (1997).  Linear Algebra Done Right, Springer. 

  9. Bak, J. & Newman, D. J. (2010). Complex Analysis, Springer-Verlag, New York.                             

  10. Betts, J. T. (2001). Practical Methods for Optimal Control Using Nonlinear   

      Programming, SIAM, Philadelphia, USA.

  1.  Berenstein, C. A. (1985). Complex Analysis; Springer-Verlag, New York.

  2. Bick, T. A. (1971 ). Introduction to Abstract Mathematics; Academic Press.

  3. Birkhoff, G. and Rota, G. (1989).  Ordinary Differential Equations; John Wiley and Sons.

  4. Boyce, W. E. & DiPrima, R. C. (2006).  Elementary Differential Equations And Boundary Value Problems, Prentice Hall, New Jersey, USA.

  5.   Brauer, F. (2006).  Some Simple Epidemic Models, Mathematical biosciences and  

  6. Brauer, F., Castillo-Chavez, C. (2012). Mathematical Models for Communicable 

  7. Brian D, Hahn, (2007). Essential MATLAB for Scientists and Engineers, Pearson Education, South Africa.

  8. Broman, A. (1970). Introduction to Partial Differential Equations; Dover, USA.

  9. Brown, J. & Churchill, R. (1996). Complex variables and applications, 7th Ed. 

  10. Brown, J. W. & Sherbert, D. R. (1984). Introductory Linear Algebra with Applications, PWS, Boston.

  11. Bryson, A. E. & Ho, Y. (1975).  Applied optimal control: Optimization, Estimation  

  12. Budak, B. M., & Fomin S. (1973). Multiple Integrals, Field Theory and Series; Mir Publishers, Moscow.

  13. Burden, R. & Faires, J. D.  (2006), Numerical Analysis, PWS Publishers

Diseases, SIAM, Philadelphia, USA.  

  1. Capinski, M. &  Kopp, E. (2005), Measure, Integral and Probability,   Springer-Verlage London Limited.                

  2. Christian, P., Nagy, J. G.  Dianne & O’Leary, D., (2006), Deblurring Images, Matrices, Spectra, and Filtering. SIAM , Philadelphia, USA.

  3. Churchill, R. V. & Brown, J. W (1990 ). Complex Variables and Applications; McGraw Hill Inc., USA.

  4. Coddington, E.A. & Levinson, N. (1983), Theory of Ordinary Differential Equations; Robert Krieger Publishing Company, Malabar, Florida.

  5. Courant, R., & John, F. (1974). Introduction to Calculus and Analysis; Vol. 2, John Wiley and Sons, USA.                         

  6. Daellenbach, H. G., George, J. A. & McNicke, D.C. (1983). Introduction to Operations Research Techniques; 2 Ed., Allyn and Bacon, Inc., USA.

  7. Datta, B. N.  (2009), Numerical Linear Algebra and Applications, SIAM, Philadelphia, USA.

  8. David, C. L. (2002). Linear Algebra and its Applications, Addison-Wesley, New York, USA.

  9. De-Lillo, N. J. (1982). Advanced Calculus with Applications; Macmillan Pub., USA.

  10. Diekmann, O. & Heesterbeek, J.A. P.  (2000). Mathematical Epidemiology of Infectious Diseases, John Wiley & Sons, West Sussex.

  11. Edwards, C. H. & Penny, D. E. (2005).  Elementary Differential Equations With Boundary Value Problems, Prentice Hall, New Jersey, USA

  12. Edwards,  C. H. & Penney, D. E. (1999). Calculus With Analytic Geometry: Early Trancendentals; 5 Prentice Hall Inc., USA.

  13. Eisberg, R.M. (2000). Fundamentals of Modern Physics, John Wiley & Sons Inc. New York.      

  14. Evans, C. L. (2010). Partial Differential Equations, American Mathematical Society.                 

  15. Fiacco, A. V. &  McCormock, G. P. (1990). Nonlinear Programming, SIAM, Philadelphia, USA.

  16. Fraleigh, J. B. (1989). A First Course in Abstract Algebra.

  17. Froberg E. (1968). Introduction to Numerical Analysis, Addison and Wesley, USA.

 Philadelphia, USA.                        

  1. Gallian, J. A.  (1990), Contemporary Abstract Algebra; D. C. Heath and Company.

  2.  Gerald, C. F. & Wheatley (2001)  Applied Numerical Analysis; Addison &Wesley, USA.

  3.  Gibarg, D. & Trudinger, N. S. (1983). Elliptic Partial Differential Equations of Second  Order; Springer-Verlag, New York.

  4. Goldstein, H. (1986).  Classical Mechanics, Addison-Wesley Publishing Company.                  

  5. Haaser, N. B. & Sullivan, J. A. (1991). Real Analysis; Dover.

  6. Halmos, P.R. (1960), Measure Theory; Springer-Verlag, New York.

  7. Hertcote , H. W. (2000). The Mathematics of Infectious Disease, SIAM Review,  Amsterdam, The Netherlands.

  8. Higham , D. J.  (2005). MATLAB Guide, SIAM, Philadelphia, USA.

  9. Hilberland, F. B. (1962). Advanced Calculus for Application; Prentice Hall, USA.

  10. Hillier, F. S. (2012). Introduction to Operations Research, McGraw Hill, Inc., USA.

  11. Hirsch, M. W, Smale, S. & Devaney, R. L. (2004).  Differential Equations,         Dynamical Systems & An Introduction to CHAOS, Elsevier Academic Press,  

  12. Hocking, L. M. (1991), Optimal Control: An Introduction to the Theory with Applications, Clarendon Press, London.

  13. Hungerford, T. W. (1974). Algebra; Springer-Verlag, New York.

 Vol 42, No. 4, December 2000, pp. 599—653.         

  1. Igor G., Nash, S. G. & Sofer A., (2009). Linear and Nonlinear  Optimization, SIAM, Philadelphia, USA.

  2. Kaufmann, J. E. (1987). College Algebra and Trigonometry; PWS Publishers, USA.

  3. Kirk , D. E., (2004), Optimal control theory: An Introduction, Dover Publications.

  4. Klages, R. & Howard, P. (2008),  Introduction to Dynamical Systems, (Lecture         Notes Version 1.2), Queen Mary University of London.

  5. Kofinti, N. K. (1997). Mathematics Beyond the Basic; Vol. 1, City Printers, Accra.

  6. Kolman, B. (1984). Introductory Linear Algebra with Applications; Macmillan Publishing Company.

  7. Kreyszig, E. (1978 ). Introductory Functional Analysis with Applications; John Wiley and Sons,  New York, U.S.A.

  8. Kudryavtsev, V. A. (1981). A Brief Course of Higher Mathematics; Mir Publishers, Moscow.  

  9. La Salle, J. P.  (1976), The Stability of Dynamical Systems, SIAM, Philadelphia, USA.

  10. Lang, S. (2012). Calculus of Several Variables, Springer-Verlag, New York.

  11.  Lenhart S., & Workman J. T., (2007), Optimal Control Applied to Biological         Systems, Chapman & Hall, New York, USA.

  12.  Lenhart, S., & Workman, J. T. (2007). Optimal Control Applied to Biological, John Wiley & Sons, New York, USA.   

  13.  Levine, I.N.  (1991). Quantum Chemistry, 4th Ed., Prentice Hill.

  14.  Levy, A. B.  (2009). The Basics of Practical Optimization, SIAM, Philadelphia,            USA.

  15. Levy, A. B. (2009). The Basics of Practical Optimization and Control, SIAM, Philadelphia, USA.

  16.  Linz, P. &  Wang, R. (2002). Exploring Numerical Methods: An Introduction to Scientific Computing Using MATLAB, Jones & Bartlett Publishers, London.

  17. Lipschuts, S.  (1975), General Topology; McGraw-Hill Book Company.

  18. Liu, J. H. (2003). A First Course in the Qualitative Theory of Differential Equations, Pearson Education, Inc., New Jersey.

  19.  Luenberger, D. G., (1996). Optimization by Vector Space Methods, John Wiley & Sons, New York, USA.    

  20. Marion, J.B. & Thornton, S.T. (1995).  Classical Dynamics of Particles and Systems, Saunder College Publishers.

  21. Marsden, J.E. (1970). Basic Complex Analysis; W.H. Freeman and Co.

  22. McCann, R. C. Introduction to Ordinary Differential Equations; Harcourt Brace Janovich, USA.

  23. McCoy, N. H. (1968). Introduction to Modern Algebra; Allyn and Bacon Inc.,

  24. Merzbacher, E.  (1986). Quantum Mechanics, 2nd Ed. John Wiley & Son Inc.

  25. Morash, R. P. (1987). A Bridge to Abstract Mathematics; Random House Inc., New York.

  26. Munem, M. A. (1989). After Calculus: Analysis; Collier Macmillan Pub. , London.

  27. Nicholson, K. W. (1986). Elementary Linear Algebra with Applications; PWS-KENT.

  28.  Ortega, J. M. (1990), Numerical Analysis, SIAM, Philadelphia, USA.

 Philadelphia, USA.

  1.  Offei, D.N.  (1970), The use of boundary condition functions for non-self-adjoint boundary value problems; I

  2.  Offei, D. N. (1969). Some asymptotic expansions of a third-order differential equations; Journal of London Mathematical Society, 44 71-87.

  3. Penny, J. & Lindfield, G.  (1995), Numerical Methods Using MATLAB, Ellis Horwood, New York.

  4. Petrovsky, I. G.(1954 ).  Lectures on Partial Differential Equations; Dover, USA.

  5. Pinchover, Y. & Rubinstein, J. (2005). An Introduction to Partial Differential Equation, Cambridge University Press.

  6. Piskunov, N. (1981). Differential and Integral Calculus; 4 Ed., Mir Publishers, Moscow.

  7.  Pliska, S. R.  (2002). Introduction to mathematical finance: Discrete time models, Blackwell Publishers Inc. 

  8.  Poole, D. (2014). Linear Algebra: A Modern Introduction, Dover, USA.

  9. Priestley, H. A. (2003). Introduction to Complex Analysis, 2nd  Ed., OUP.

  10. Redheffer, R. (1992). Introduction to Differential Equations; Jones & Bartlett Pub., Inc.

  11.  Roberts, A. J.  (2009), Elementary Calculus of Financial Mathematics, SIAM, Philadelphia, USA.

  12.  Rofman, J. J. (2015). Advanced Modern Algebra, American Mathematical Society.

  13. Roman, S. (2005), Advanced Linear Algebra, 2nd edn; Springer-Verlag, New York.

  14. Ross, S. L. (1984). Differential Equations; 3 Ed., John Wiley & Sons, USA.

  15. Rudin, W. (1974), Principles of Mathematical Analysis; McGraw-Hill Book Company.

  16. Savin, A. & Sternin, B. (2017). Introduction to Complex Theory of Differential Equations, Birkhauser.

  17.  Scheid, F.  (1988). Numerical Analysis (Schaum Series); McGraw Hill, USA.

  18. Schiff, L.I. (1988). Quantum Mechanics, 3rd Ed., McGraw Hill, New York.

  19. Simmon, G.F. (1973), Introduction to Topology and Modern analysis; McGraw-Hill. 

  20. Smith, K. L. (1988). College Mathematics and Calculus With Applications to Management, Life and Social Sciences; Brooks/Cole Publishing Co., California, USA.

  21. Speyer,  J. L. & Jacobson, D. H. (2010). Primer on Optimal Control Theory, SIAM.

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  23. Spiegel, M.R. (1992), Real Variables:  Lebesque Measure and Integration with Applications to Fourier Series; MacGraw-Hill  

  24. Spiegle, M. R. (1991). Advanced Calculus; McGraw Hill, USA.

  25. Stewart J. (1983). Single Variable Calculus; PWS, USA.

  26. Stewart, J. (1987). Calculus; Wadsworth Inc.

  27. Stewart, J. (2003). Calculus (Early Transcendental), 6th Ed. Thomson Brooks/Cole.

  28. Strang, G. (2006). Linear algebra and Its Applications, Thomson Brookes/Cole,  

California, USA.

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Sons Inc. New York. 

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Programming, Springer, New York, USA. 

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  and Schmidt, Boston, USA.

  1. Symon, K.R.  (1973). Mechanics, Addison-Wesley Publishing Company

      Systems, Chapman & Hall, New York, USA.

  1. Taylor, A.E. & Lay, D.C.  (1988), Introduction to Functional  analysis; John Wiley 

 and Sons.

  1. Teschle, G., (2010). Ordinary Differential Equations and Dynamical Systems:  

 Graduate Studies in Mathematics, AMS Vol 140, Providence, Rhode Island, USA

  1. Thomas, G. B. and Finney, R. L. (1996). Calculus and Analytic Geometry; 9 Ed. 

 Addison-Wesley Pub., Reading, USA.

  1. Titchmarsh, E.C. (1972), Eigenfunction expansions associated with second-order 

 differential equations; Oxford University Press.

  1. Trefethen, L. N., &  Bau, D. ( 1997). Numerical Linear algebra ,SIAM, Philadelphia, 

USA.

  1. Winston, W. L. (1994). Operations Research: Applications and Algorithms; 3rd Ed., 

Duxbury Press, Belmont, USA.

  1. Winter, R.G. (1986).  Quantum Physics, 2nd Ed., Faculty Publishing Inc.

Zill, G. D. (2012). A First Course in Differential Equations with Modelling Applications, John Wiley and Sons.

Entry Requirements: 

Applicants pass Elective Mathematics, Economics and any one (1) of the following elective subjects: Physics, Chemistry Business Management, Principles of Costing and Accounting or Geography.

Career Opportunities: 

This programme combines the main contents of both economics and mathematics within a programmatic structure that joins the two disciplines.  77    It applies mathematical methods to represent theories and analyse problems in economics.    It is argued that mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects. In addition, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without it. Therefore a combination of both disciplines in a single programme ensures that our graduates enter the world of work with the requisite skills.

Programme Structure

Level 100

First Semester

CMS 107: Communicative Skills I
3 Credit(s)

Engaging in academic work at the university is challenging. This course is aimed at equipping fresh students to make the transition from pre-university level to the university level. It assists them in engaging and succeeding in complex academic tasks in speaking, listening, reading and writing. It also provides an introduction to university studies by equipping students with skills that will help them to engage in academic discourse with confidence and fluency.

Second Semester

CMS 108: Communicative Skills II
3 Credit(s)

This is a follow-up course on the first semester one. It takes students through writing correct sentences, devoid of ambiguity, through the paragraph and its appropriate development to the fully-developed essay. The course also emphasizes the importance and the processes of editing written work.

Level 400

First Semester

MAT 401: Real Analysis I
3 Credit(s)
Pre-requisite: MAT 302 and MAT 303

This course is designed as a basic introductory course in the analysis of metric spaces. It is aimed at providing the abstract analysis components for the degree course of a student majoring in mathematics. This course affords students an opportunity to gain some familiarity with the axiomatic method in analysis. The topics to be covered are: metric spaces, open spheres, open sets, limit points, closed sets, interior, closure, boundary of a set, sequences in metric spaces, subsequences, upper and lower limits of real sequences,  continuous functions on metric spaces, uniform continuity, isometry, homomorphism, complete metric spaces, compact sets in a metric space, Heine-Borel theorem, connected set, and the inter-mediate value theorem.
MAT 405: Ordinary Differential Equations
3 Credit(s)
Pre-requisite: MAT 301

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics  covered include linear differential equation of order n with coefficients continuous on some interval J,  existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters,  Wronskian matrix of n independent solutions of a homogeneous linear equation,  ordinary and singular points for linear equations of the second order,  solution near a singular point, method of Frobenius, singularities at infinity, simple examples of  Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument; Legendre, Bessel, Chebyshev, Hypergeometic functions and  orthogonality properties.
MAT 409: Operations Research
3 Credit(s)
Pre-requisite: MAT 206

This course serves as an introduction to the field of operations research. It will quip students with scientific approaches to decision-making and mathematical modelling techniques required  to design, improve and operate complex systems in the best possible way. Topics covered include linear programming, the simplex method, duality and sensitivity analysis, integer programming , nonlinear programming, dynamic programming and  network models. 

Second Semester

MAT 408: Introductory Functional Analysis
3 Credit(s)
Pre-requisite: MAT 401

This course is intended to introduce the student to the basic concepts and theorems of functional analysis and its applications. Topics covered include linear spaces, topological spaces, normed linear spaces & Banach Spaces, inner product spaces,  Hilbert spaces, linear functional and the Hahn-Banach theorem.