NON-BSCM STUDENTS
Topics & Recommended
Readings of Servicing Courses
Topics covered
- Space and geometry
- Vectors, angles, and motions of the plane
- Planar symmetry: rosettes, whirls, friezes and wallpapers
- Symmetry in art: rugs, Chinese lattices, the work of Escher
- Aesthetic trade-offs
- Homothecies, similarities and affinities
- Conics and their eclosion in baroque art
- Mathematics and music: the geometry of canons, symmetry in music
- Perspective
- Drawing systems
- Projective and hyperbolic geometry
- Non-Euclidean symmetries
- Rule-driven creation
Recommended Readings
- Bruter, Claude.Mathematics and Art. Springer, 2002
- Cromwell, Peter. R.Polyhedra. Cambridge University Press. 1999
- Cucker, Felipe.Manifold Mirrors: The Crossing Paths of the Arts and Mathematics. Cambridge University Press, 2013
- Emmer, Michele (Ed).The Visual Mind: Art and Mathematics. Cambridge: MIT Press, 1993
- Emmer, Michelle (Ed). The Visual Mind: Art and Mathematics: Vol. 2. MIT Press 2005
- Kalajdzievski, Sasho. Math and Art: An Introduction to Visual Mathematics. Chapman and Hall, 2008
- Kappraff, Jay. Connections, The Geometric Bridge between Art and Science. World Scientific Pub Co Inc. 2002
- Kinsey, L. Christine and Teresa E. Moore.Symmetry, Shape and Space. Key College. 2006
- Pedoe, Dan. Geometry and the Visual Arts. Dover Publications. 2011
- Washbourn, Dorothy K. and Donald W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. University of Washington Press. 1991
- Weyl, Hermann. Symmetry. Princeton University Press. 1983
Online Resources
Topics covered
- Polynomials; Mathematical induction; Binomial theorem
- Coordinate geometry and conic sections; Basic trigonometry
- Functions and inverses; Limits, Continuity and differentiability
- Techniques of differentiation, implicit, logarithmic and parametric differentiation; Successive differentiation
- Applications of differentiation: rate of change, local extrema, optimization problems, Taylor's series, De l’H?pital rule
Recommended readings
Text(s):
- a. Frank Ayres, Jr. and Elliott Mendelson, Calculus (Schaum's Outlines), 6th ed., McGraw Hill, 2013
b. Fred Safier, Precalculus (Schaum's Outlines), 3rd ed., McGraw Hill, 2013 - Basic Calculus and Linear Algebra (Compiled by Department of Mathematics, City University of Hong Kong), Pearson Custom Publishing, 2007 (Available at CityU Bookstore)
Note: This book is compiled from:- Thomas' Calculus (11th Ed.) by George B. Thomas, Maurice D. Weir, Joel D. Hass, & Frank R. Giordano. (Chapters 1–8, 10–12, selected appendices)
- Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire (Chapters 1–3)
- Ron Larson and Bruce Edwards, Calculus I with Precalculus: A One-Year Course, 3rd ed., Brooks/Cole, 2012
- C. Henry Edwards and David E. Penney, Calculus: Early Transcendentals, 7th ed., Pearson Prentice Hall, 2008
- Robert A. Adams, Calculus: A Complete Course, 6th ed., Pearson Addison Wesley, 2006
- Glyn James, Modern Engineering Mathematics, 4th ed., Pearson Prentice Hall, 2008
Topics covered
- Definite and indefinite integrals; Techniques of integration, integration of rational functions, integration by substitution, integration by parts
- Physical and geometric applications of integration
- Vectors in R2 and R3; Scalar products, vector products, triple scalar products; Linear (in)dependence
- Matrices; Determinants, cofactor expansion; Systems of linear equations, Gaussian elimination, Cramer’s rule; Matrix inverses, Gauss-Jordan elimination method
- Arithmetic of complex numbers; Polar and Euler forms; De Moivre’s theorem and its applications
Recommended readings
Text(s):
- a. Frank Ayres, Jr. and Elliott Mendelson, Calculus (Schaum's Outlines), 6th ed., McGraw Hill, 2013
b. Fred Safier, Precalculus (Schaum's Outlines), 3rd ed., McGraw Hill, 2013 - David C Lay, Linear Algebra and its applications, 3rd Pearson International Edition, 2006
- Basic Calculus and Linear Algebra (Compiled by Department of Mathematics, City University of Hong Kong), Pearson Custom Publishing, 2007
Note: This book is compiled from:- Thomas’ Calculus (11th Ed.) by George B. Thomas, Maurice D. Weir, Joel D. Hass, & Frank R. Giordano. (Chapters 1–8, 10–12, selected appendices)
- Linear Algebra: A First Course in Pure and Applied Math by Edgar G. Goodaire (Chapters 1-3)
- C. Henry Edwards and David E. Penney, Calculus: Early Transcendentals, 7th ed., Pearson Prentice Hall, 2008
- Robert A. Adams, Calculus: A Complete Course, 6th ed., Pearson Addison Wesley, 2006
- Glyn James, Modern Engineering Mathematics, 4th ed., Pearson Prentice Hall, 2008
Topics covered
- Polynomials; Mathematical induction
- Coordinate geometry and conic sections; Basic trigonometry
- Functions and inverses
- Limits of sequences and infinite series
- Limits, continuity and differentiability of functions
- Techniques of differentiation, implicit, logarithmic and parametric differentiation; Successive differentiation
Recommended Textbook
Single Variable Calculus (6th edition) by J. Stewart, Thomson Brooks/Cole, 2009
Topics covered
- Basic theorems of differentiation
- Applications of differentiation: rate of change, local extrema, optimization problems, power and Taylor series, l’H?pital rule
- Definite and indefinite integrals; Techniques of integration, integration by substitution, integration by parts; Improper integrals
- Physical and geometric applications of integration
- Vectors in R2 and R3; Scalar products, cross products, triple scalar products; Linearly (in)dependence; Applications to equations of lines and planes
- Matrices; Determinants, cofactor expansion; Systems of linear equations, Gaussian elimination, Cramer’s rule; Matrix inverses, Gauss-Jordan elimination method
- Arithmetic of complex numbers; Polar and Euler forms; De Moivre’s theorem and its applications
Recommended Textbook (tentative)
- Single Variable Calculus (7th edition) by J. Stewart, Pacific Grove, CA: Brooks/Cole, 2011.
- Modern Engineering Mathematics (4th edition) by G. James, Upper Saddle River, NJ: Prentice Hall, 2010.
Keyword syllabus
- Linear Algebra: Orthogonality; Eigenvalues and eigenvectors; Eigenvalue decompositions.
- Multi-variable Calculus: Functions of several variables; Partial differentiation; Multi-variable Taylor series; Multiple integration; Gradient, divergence and curl; Line and surface integrals; Theorems of Gauss, Stokes and Green.
Textbook
Mathematics for Engineering and Science, Department of Mathematics, City University of Hong Kong, Prentice Hall, Pearson Education South Asia, 2008
Note: This book is compiled from:
- Calculus – Early Transcendentals (7th ed.) by C. Henry Edwards & David E. Penny (Chapters 11, 12, 13 and 14)
- Linear Algebra – A Pure and Applied First Course (1st ed.) by Edgar G. Goodaire (Chapters 1, 2, 3, 7, Solutions to True/False Questions)
- Differential Equations and Boundary Value Problems (4th ed.) by C. Henry Edwards & David E. Penny (Chapters 1, 3, 9 and Answers to Selected Problems)
Reference
- Thomas’, Calculus (13th ed.) by George B. Thomas, Maurice D. Weir, Joel D. Hass and Frank R. Giordano, Upper Saddle River, N.J.: Pearson Addison Wesley, 2014
- Linear Algebra and Its Applications (4th ed.) by David C. Lay, Pearson, 2012
- Advanced Engineering Mathematics (7th ed.) by Peter V. O'Neil, Cengage Learning, 2012
- Advanced Engineering Mathematics (10th ed.) by Erwin Kreyszig, Wiley 2011
Keyword syllabus (as shown in Form 2B)
Introduction to Computer Systems, Numerical tools, Statistical packages and Mathematical packages.
Topics covered
The Use of EXCEL
- Introduction to EXCEL workplace; Probability Distributions, histogram, random number generation; Statistical Inference; Regression and Correlation; ANOVA
The Use of MATLAB
- Introduction to MATLAB workplace; Solving of system of linear equations; basic commands in MATLAB, random number generation, elementary MATLAB programming techniques
Reference books
- Elementary Statistics (11th Ed.) by R. Johnson & P. Kuby, Duxbury, Brooks/Cole Cengage Learning, 2012
- Elementary Statistics Using Excel (4th Ed.) by M F Triola, Addison Wesley, 2010
Keyword syllabus (as shown in Form 2B)
Mathematical logic. Methods of mathematical proof. Predicate calculus. Sets and relations. Castesian product. Functions. Permutations and combinations. Inclusion-exclusion principle. Recurrence relations. Complexity analysis of algorithms.
Topics covered
Mathematical logic
- Basic concepts, propositions and logical operators, algebra of propositions, predicates and quantifiers, logical equivalence, logical inference, valid arguments, inference rules
Methods of proving theorems
- Direct proof, indirect proof, prove by contradiction, conditional proof, proof by cases, mathematical induction
Basic set theory
- Elements, equality of sets, subsets, Venn diagrams, power set, algebra of sets, set operators, set identities, Cartesian product
Relations
- Binary relations, n-ary relations, representations of relations, reflexive relations, symmetric relations, antisymmetric relations, transitive relations, composite relation, inverse relation
Functions
- Basic definitions, composite function, injective surjective and bijective functions, inverse function
Combinatorics
- Pigeonhole principle, product rule, sum rule, selections with and without replacement, permutations, combinations, binomial coefficients, inclusion-exclusion principle
Recurrence relations
- Linear homogeneous recurrence relations with constant coefficients, characteristic polynomial, Solutions of special linear nonhomogeneous recurrence relations
Analysis of algorithms
- Computation of maximum number of operations of some simple algorithms
Suggested book
Discrete Mathematics And Its Applications (6th Ed.) by Kenneth H. Rosen, McGraw-Hill Edition
Keyword syllabus (as shown in Form 2B)
Eigenvalues and eigenvectors. Applications in elasticity. First-and second-order ordinary differential equations and applications. Vector calculus. Partial differentiation. Multiple integration. Gradient, divergence and curl. Theorems of Gauss, Stokes and Green. Applications in energy methods, stress and strain transformations, etc. Fourier series.
Topics covered
Eigenvalues and Eigenvectors
- Determination of Eigenvalues and Eigenvectors, diagonalization
Ordinary Differential Equations
- Methods for solving first-order ODEs, homogeneous second-order ODEs, solving second-order ODEs by method of undetermined coefficients and method of variation of parameters, higher-order ODEs
Multivariable Calculus
- Limit, continuity and partial derivative, partial differentiation, chain rule, implicit function theorem, Taylor’s theorem, Maxima and minima, directional derivative and gradient
Vectors Differential Calculus
- Vector fields, divergence of a vector field, curl of a vector field, vector identities
Multiple Integrals
- Double integrals in Cartesian coordinates, change of variable in double integrals; triple integrals in Cartesian coordinates, change of variable in triple integrals
Vector Integral Calculus
- Line integrals, conservative fields; Surface integrals; Divergence theorem; Theorems of Stokes and Green, applications
Fourier Series
- Fourier series for periodic, even and odd functions, half range series
Textbook
Mathematics for Engineering and Science, Department of Mathematics, City University of Hong Kong, Prentice Hall, Pearson Education South Asia, 2008
Note: This book is compiled from:
- Calculus – Early Transcendentals (7th Ed.) by C. Henry Edwards & David E. Penny (Chapters 11, 12, 13 and 14)
- Linear Algebra – A Pure and Applied First Course (1st Ed.) by Edgar G. Goodaire (Chapters 1, 2, 3, 7, Solutions to True/False Questions)
- Differential Equations and Boundary Value Problems (4th Ed.) by C. Henry Edwards & David E. Penny (Chapters 1, 3, 9 and Answers to Selected Problems)
References
-
Differential Equations with Boundary-Value Problems (6th ed.) by Zill, Dennis G. and Cullen, Michael R., Belmont, CA: Thomson Brooks/Cole, 2005
-
Thomas’ Calculus (11th Ed.) by Thomas, George B., Weir, Maurice D., Hass, Joel D. and Giordano, Frank R., Upper Saddle River, N.J.: Pearson Addison Wesley, 2004
Keyword syllabus (as shown in Form 2B)
Complex numbers. Vectors, matrices and determinants. Linear dependence, orthogonality. Systems of linear equations. Eigenvalues and eigenvectors. Functions of several variables. Partial differentiation. Taylor series. Double integrals
Textbook
Mathematics for Engineering and Science, Department of Mathematics, City University of Hong Kong, Prentice Hall, Pearson Education South Asia, 2008
Note: This book is compiled from:
- Calculus – Early Transcendentals (7th ed.) by C. Henry Edwards & David E. Penny (Chapters 11, 12, 13 and 14)
- Linear Algebra – A Pure and Applied First Course (1st ed.) by Edgar G. Goodaire (Chapters 1, 2, 3, 7, Solutions to True/False Questions)
- Differential Equations and Boundary Value Problems (4th ed.) by C. Henry Edwards & David E. Penny (Chapters 1, 3, 9 and Answers to Selected Problems)
Reference
- Thomas’, Calculus (11th ed.) by George B. Thomas, Maurice D. Weir, Joel D. Hass and Frank R. Giordano, Upper Saddle River, N.J.: Pearson Addison Wesley, 2004
- Linear Algebra and Its Applications (3rd ed.) by David C. Lay, Pearson, 2006
- Multivariable Calculus with Matrices (6th ed.) by C. Henry Edwards and David E. Penney, Prentice Hall, 2002
- Elements of Advanced Engineering Mathematics by Peter V. O'Neil, Cengage Learning, 2010
Keyword syllabus (as shown in Form 2B)
Random variables. Distribution. Data and sample description. Estimation of parameters. Tests of hypothesis. Regression. ANOVA.
Topics covered
Probability
- Basic concepts, rules of probability, conditional probability, Bayes’ Rule
Probability Distribution (discrete variables)
- Discrete probability distributions, binomial random variable
Normal Probability Distributions
- Normal probability distributions and its applications
Sample Variability
- Central limit theorem
Introduction to Statistical Inferences
- Basic concepts of estimation and hypothesis testing, classical and probability approach
Inferences Involving One Population
- Confidence intervals, inference about population mean, inference about the binomial probability of success, t test, inference about the population standard deviation, chi-square distribution
Inferences Involving Two Populations
- Independent and dependent samples; Comparison on two populations using the mean of paired differences, the difference between two means and the ratio of two variances, F test
Linear Correlation and Regression Analysis
- Linear correlation and regression analysis, line of best fit, confidence interval estimations
ANOVA* (*to be covered if time permits)
Suggest books
- Elementary Statistics (11th Ed.) by R. Johnson & P. Kuby, Duxbury, Thomson Learning, 2012
- Elementary Statistics Using Excel (6th Ed.) by M F Triola, Addison Wesley, 2018
Keyword syllabus (as shown in Form 2B)
Ordinary differential equations. Fourier series. Laplace transforms. Random variables. Probability. Distributions. Data and sample description. Estimation of parameters. Test of hypothesis. Simple linear regression.
Topics covered
Ordinary Differential Equations
- Methods for solving first-order ODEs, homogeneous second-order ODEs, solving second-order ODEs by method of undetermined coefficients and method of variation of parameters
Fourier Series
- Fourier series for periodic, even and odd functions, half range series
Laplace Transforms
- Definition and the Inverse Laplace Transform, properties of Laplace Transform
Probability Distribution
- Random variables, discrete probability distributions, normal probability distributions
Sample Variability
- Central limit theorem
Statistical Inferences
- Basic concepts of estimation and hypothesis testing, confidence intervals, statistical inferences
Simple Linear Regression
Suggested books
- Mathematics for Engineering and Science, Department of Mathematics, City University of Hong Kong, Prentice Hall, Pearson Education South Asia, 2008
- Advanced Engineering Mathematics (9th Ed.) by Erwin Kreyszig, Wiley, 2006
- Elementary Statistics (11th Ed.) by R. Johnson & P. Kuby, Duxbury, Thomson Learning, 2012
- Elementary Statistics Using Excel (4th Ed.) by M F Triola, Addison Wesley, 2010
Keyword syllabus (as shown in Form 2B)
Eigenvalues and eigenvectors. First- and higher order ordinary differential equations. Partial differentiation. Laplace transforms. Fourier series.
Topics covered
Eigenvalues and Eigenvectors
- Determination of Eigenvalues and Eigenvectors, diagonalization
Ordinary Differential Equations
- Methods for solving first-order ODEs, homogeneous second-order ODEs, solving second-order ODEs by method of undetermined coefficients and method of variation of parameters, higher-order ODEs
Multivariable Calculus
- Limit, continuity and partial derivative, partial differentiation, chain rule, Taylor’s theorem, Maxima and minima
Laplace Transforms
- Definition and the Inverse Laplace Transform, properties of Laplace Transform
Fourier Series
- Fourier series for periodic, even and odd functions, half range series
Textbooks
Mathematics for Engineering and Science, Department of Mathematics, City University of Hong Kong, Prentice Hall, Pearson Education South Asia, 2008
Note: This book is compiled from:
- Calculus – Early Transcendentals (7th Ed.) by C. Henry Edwards & David E. Penny (Chapters 11, 12, 13 and 14)
- Linear Algebra – A Pure and Applied First Course (1st Ed.) by Edgar G. Goodaire (Chapters 1, 2, 3, 7, Solutions to True/False Questions)
- Differential Equations and Boundary Value Problems (4th Ed.) by C. Henry Edwards & David E. Penny (Chapters 1, 3, 9 and Answers to Selected Problems)
References
Advanced Engineering Mathematics (9th Ed.) by Erwin Kreyszig, Wiley 2006
Topics Covered
Mathematical Logic, Set Theory, Counting and Probability, Number Theory, and Graph
Textbook
1. K. Bogart, C. Stein, R. L. Drysdale, Discrete Mathematics for Computer Science, Key College Publishing, 2006
2. K. H. Rosen, Discrete Mathematics and Its Applications, 7th Edition, McGraw Hill, 2012
Keyword syllabus (as shown in Form 2B)
- Ordinary differential equations: First order differential equations, Second and higher order linear differential equations; Laplace transform; System of linear differential equations.
- Partial differential equations: Diffusion, wave and Laplace equations; Initial value problems; Fourier series; Boundary value problems.
Recommended readings
Text(s):
- "Differential Equations & Linear Algebra", 2nd ed.
By Farlow, Hall, McDill and West
Publisher: Pearson Education - "Differential Equations with Boundary-value Problems", 7th ed.
By D. G. Zill, M. R. Cullen
Publisher: Brooks/Cole – CENGAGE Learning
Keyword syllabus (as shown in Form 2B)
Probability. Random variables. Distributions. Stochastic processes. Queuing theory.
Topics covered
Elementary Probability
- Probability: Probability, independence, conditional probability, expectation
- Random variables: a random variable, random vector, conditional random variable, conditional expectation
- Distributions: Bernoulli trials, binomial distribution, Poisson distribution, uniform distribution, exponential distribution
Stochastic Processes
- Poisson processes
- Markov chains
Queuing Theory
- Little’s formula, balance equations, m/m/1 queue, m/m/k queue
References
- Introduction to probability models / Sheldon M. Ross / 9th ed. / Academic Press, c2007