MATH 280 SAT4 Linear and Nonlinear Optimization


Schedule: 05:00 PM - 08:00 PM Sat, IB 104
Course Description: Fundamentals of optimization, simplex method, duality and sensitivity, interior point methods, unconstrained optimization, optimality conditions for constrained problem, and feasible-point methods.
Credit: 3 units
Prerequisite: COI
Consultation: 01:00 PM - 04:00 PM Tue, Wed, Thu & Fri; CS Dean’s Office, IB Building, or by Appointment. In sending emails, please use the subject: MATH 280 Consultation
Link to Course Syllabus
Link to Course Notes (Updated: 07 February 2026)

Theory and Machine Exercises (deadline of submission in parenthesis):
Final Examination (TBA)






MATH 140 ZZ Topological Structures


Schedule: 06:00 AM - 07:30 PM Tue & Thu, KA 402
Course Description: The topology of the real line; the axioms for a topological space and the elementary properties of a topological space; continuity, connectedness and compactness; construction of topological spaces.
Credit: 3 units
Prerequisite: JS (Junior Standing)
Consultation: 01:00 PM - 04:00 PM Tue, Wed, Thu & Fri; CS Dean’s Office, IB Building, or by Appointment. In sending emails, please use the subject: MATH 140 Consultation

Exercises (deadline of submission in parenthesis):
Schedule of Examinations
Link to Course Syllabus
Link to Course Notes (Updated: 12 Feb 2026)
Course Topics:
  1. Set Theory and Logic: Fundamental Concepts, Functions and Relations, Finite Sets, Countable and Uncountable Sets, Infinite Sets and the Axiom of Choice, Partially Ordered Sets and Well-Ordered Sets
  2. Topological Spaces and Continuous Functions: Topological Spaces, Basis for a Topology, Order Topology, Product Topology, Subspace Topology, Closed Sets and Limit Points, Continuous Functions, Metric Topology
  3. Connectedness and Compactness: Connected Spaces, Connected Spaces on the Real Line, Compact Spaces, Compact Spaces on the Real Line
  4. Countability and Separation Axioms: Countability Axioms, Separation Axioms, Normal Spaces, Urysohn Lemma







MATH 237 SAT3 Functional Analysis


Schedule: 01:30 PM - 04:30 PM Sat, IB 104
Course Description: Banach spaces; review of Lebesgue integration and Lp spaces; foundations of Linear operator theory, nonlinear operators; the contraction mapping principle; nonlinear compact operators and monotonicity; the Schauder Fixed Point Theorem; the Spectral Theorem.
Credit: 3 units
Prerequisite: Math 232 (Real Analysis) / equiv
Consultation: 09:00 AM - 12:00 PM Tue and Thu, 03:00 PM - 05:00 PM Wed and Fri; CS Dean’s Office, IB Building, or by Appointment. In sending emails, please use the subject: MATH 237 Consultation

Exercises (deadline of submission in parenthesis):
Course Topics (Link to Course Syllabus, Link to Course Notes):
  1. Fundamental Concepts: Topological, Metric, Seminormed, Normed Spaces, Banach Fixed Point Theorem, Inner Product Spaces, Hilbert Spaces
  2. Function Spaces: Spaces of Bounded, Continuous, Continuously Differentiable, and Hölder Continuous Functions, Measure Theory, Lebesgue–Bochner Integral, Strongly Measurable Functions, Lebesgue Spaces, Sobolev Spaces
  3. Density, Convexity, and Compactness: Dense Subsets of Lebesgue Spaces, Convolutions, Mollifiers, Dense Subsets of Sobolev Spaces
  4. Linear Operators: Bounded Linear Operators, Riesz Representation Theorem, Lax–Milgram Lemma, Generalizations of the Lax–Milgram Lemma, Hahn–Banach Theorem, Dual of Lebesgue Spaces, Dual Spaces of Continuous Functions
  5. Baire Category Theorem and Its Consequences: Baire Category Theorem, Uniform Boundedness Principle, Open Mapping Theorem, Closed Graph Theorem
  6. Weak and Weak-Star Topologies: Weak Topology, Weak Convergence, Weak and Weak-Star Topologies of the Dual Space, Reflexive Spaces
  7. Introduction to Spectral Theory: Hamel Basis, Schauder Basis, Orthonormal Basis, Riesz Basis Spectra, Resolvents, Fredholm Operators, Compact Operators, Self-Adjoint Operators, Closed Operators and their Extensions (optional)
  8. Monotone and Continuous Nonlinear Operators (if time permits): Modes of Monotonicity and Continuity, Schauder Fixed Point Theorem







MATH 134 X Complex Analysis


Schedule: 01:30 PM - 03:00 PM Tue & Thu, IB 103
Course Description: Topology of the complex plane; continuous and differentiable complex functions; power series functions; integration; Cauchy’s theorem; local analysis.
Credit: 3 units
Prerequisite: Math 55 (Elementary Analysis III)
Consultation: 09:00 AM - 12:00 PM Tue and Thu, 03:00 PM - 05:00 PM Wed and Fri; CS Dean’s Office, IB Building, or by Appointment. In sending emails, please use the subject: MATH 134 Consultation

Exercises (deadline of submission in parenthesis):
Schedule of Examinations
Link to Course Syllabus
Link to Course Notes (Updated on: 23 November 2025)
Course Topics:
  1. Complex Numbers: Preliminaries, Introduction to Complex Numbers, Properties of Complex Numbers, Complex Numbers and the Argand Plane, The Triangle Inequality, Polar Coordinates, Integer and Fractional Powers of a Complex Number, Some Topology on the Complex Plane
  2. Analytic Functions: Introduction to the Complex Function, Limits and Continuity, The Complex Derivative, Theorems, Uniqueness, Cauchy-Riemann Equations, Analyticity, Harmonic Functions
  3. Elementary Functions: Exponential Functions, Trigonometric Functions and Hyperbolic Functions, Logarithmic Functions, Inverse Trigonometric Functions, Inverse Hyperbolic Functions
  4. Integrals: Contour Integrations and Green’s Theorem, Cauchy Integral Theorem: Proof, Consequences, Corollaries, Path Independence and Indefinite Integrals, Cauchy Integral Formula, Extensions and Consequences of Cauchy Integral Formula
  5. Series: Convergence of Sequences and Series, Power Series and Taylor Series, Techniques for Obtaining Taylor Series Expansions, Laurent Series
  6. Residues and Poles: Definition of the Residue, Residue Theorems, Isolated Singularities, Finding the Residue, Residue Theorem and Evaluation of Complex Integrals, Evaluation of Real Integrals with Residue Calculus, Applications
Reference Text: J. M. Brown and R. V. Churchill, Complex Variables and Applications, 9th edition, McGraw-Hill, New York, 2014.