| Semester taken | Course Code & Name | Lecturer(s) | Textbook (if any) | Material covered | Mark |
|---|---|---|---|---|---|
| 2003/1 | MATH1061 - Discrete Mathematics | Diane Donovan & Barry Jones | Epp | Elementary logic, number theory, counting, set theory, graph theory, binary operations and recursion. | 7 (High Distinction) |
| 2003/1 | MATH1051 - Calculus and Linear Algebra | Eliot Tonkes & Graeme Chandler | Stewart | Vectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, vector product, eigenvalues, eigenvectors, applications. Equation of straight line & plane. Extreme value theorem, maxima & minima. Sequences, series, Taylor series, L'Hopital's rules. Techniques of integration, numerical methods, volumes of revolution. | 7 (High Distinction) |
| 2003/2 | MATH1052 - Multivariate Calculus and Ordinary Differential Equations | Eliot Tonkes, Jan Chabrowski & Barry Jones | Stewart | Vector calculus, arclength, line integrals, applications. Calculus of 2 & 3 variables: partial derivatives, conservative fields, Taylor series, maxima & minima, nonlinear equations. 1st order & linear 2nd order differential equations (constant coefficients). Applications (dynamical systems etc), numerical methods. | 7 (High Distinction) |
| 2003/2 | MATH1070 - Frontiers of Computational Science | Peter Adams, Bernard Pailthorpe & Ben Skellet | Computational science in cryptography, scientific computing and complex systems. | 7 (High Distinction) | |
| 2004/1 | MATH2000 - Calculus and Linear Algebra II | Mike Pemberton & Phil Isaac | Kreyszig[1] | ODEs, Surface and Volume Integrals, Stokes' and Green's Theorems. Solution of Linear Systems, Vector and Matrix Norms, numerical algorithms for Eigensystems. | 7 (High Distinction) |
| 2004/1 | STAT2003 - Probability and Statistics | Phil Pollett | Probability; random variables; probability distributions; Markov processes; statistical analysis & modelling. | 7 (High Distinction) | |
| 2004/1 | MATH2400 - Mathematical Analysis | Jan Chabrowski | Bounded & monotone sequences. Sequences & series of real functions. Intermediate & mean value theorems, iterative procedures. Taylor's Theorem & error estimates, criteria for integrability, vector functions on R^n : continuity & differentials. Implicit & Inverse Function Theorems & applications. Multiple integrals on R^n. | 7 (High Distinction) | |
| 2004/2 | MATH2100 - Applied Mathematical Analysis | Cathy Holmes & Tony Bracken | Kreyszig[1] | Systems of ODEs, Laplace Transforms, Fourier Series, PDEs. | 7 (High Distinction) |
| 2004/2 | MATH2200 - Scientific Computing | Nicole Bordes & Tianhai Tian | Matlab programming. Algorithms for nonlinear equations, linear systems, data fitting, integration and differentiation, ordinary differential equations - initial and boundary value problems. | 7 (High Distinction) | |
| 2004/2 | MATH2300 - Linear Algebra and Graph Theory | Melinda Buchanan and Peter Jenkins | Vector Spaces, bases, linear transformations, eigensystems. Basic graph theory, graph factorisation, graph colouring. | 7 (High Distinction) | |
| 2004/2 | MATH3306 - Set Theory and Logic | Victor Scharaschkin & Steve Watson | Naive Set Theory, Russell's paradox. ZFC axioms. Definition of relations, functions, natural numbers, rationals and reals. Partially, total and well ordered sets. Zorn's Lemma and the Axiom of Choice and its consequences. Ordinal numbers. Recursion. Cardinal Numbers. Propositional Logic. First Order Logic. Peano axioms. Soundness. Completeness. Godel's Theorems. | 7 (High Distinction) | |
| 2004/05 | Summer Research - General Topology | Victor Scharaschkin | Munkres | Point Set Topology | NA |
| 2005/1 | MATH3302 - Coding and Cryptography | Peter Adams & Barbara Meinhaut | Error correction & detection. Hamming, BCH, Reed-Solomon & cyclic codes. Cryptographic methods for encryption, decryption & authentication. DES, IDEA, RSA. Project - Mental Poker. | 7 (High Distinction) | |
| 2005/1 | MATH3303 - Abstract Algebra & Number Theory | Elizabeth Billington | Fraleigh | Groups, permutation groups, dihedral groups. Isomorphism theorems, Burnside's lemma, Sylow theorems. Rings, Ideals, Euclidean domains. Polynomial factorization algorithms. Field extensions, splitting fields. Euler phi function, Fermat's little theorem, Chinese remainder theorem, Polynomial congruences, Legendre symbol, quadratic residues, quadratic congruence, Gauss' lemma and quadratic reciprocity. | 7 (High Distinction) |
| 2005/1 | MATH3401 - Complex Analysis | Phil Diamond | Spiegel | Complex Numbers, Analytic Functions, Elementary Functions, Mapping by Elementary Functions, Integrals, Cauchy's Theorem, Power and Laurent Series, Residues and Poles, Conformal Mapping. | 7 (High Distinction) |
| 2005/1 | MATH3402 - Functional Analysis | Min-Chun Hong | Metric Spaces. Topological Spaces, compactness, connectedness, completeness, contraction mappings. Norms, Normed linear spaces. | 7 (High Distinction) | |
| 2005/2 | MATH3103 - Algebraic Methods of Mathematical Physics | Mark Gould | Lie groups and algebras. Representation theory and applications to physics. | 7 (High Distinction) | |
| 2005/2 | MATH4301 - Advanced Algebra | Victor Scharaschkin | Groups: normal series, solvable and nilpotent groups. Group actions. Review of rings and fields. Normal and separable extensions of fields. Galois theory: the Galois group, the correspondence between subgroups and extensions. Solvability by radicals, construction of regular polygons etc. Galois groups of finite fields. Explicit calculation of Galois groups. Infinite Galois Theory. | 7 (High Distinction) | |
| 2005/2 | MATH4404 - Advanced Functional Analysis | Phil Diamond | Kreyszig[2] | Normed spaces, Linear operators. Dual spaces, weak and strong convergence. Hilbert spaces, Riesz's representation theorem. Hahn-Banach theorem, Uniform boundedness theorem, Open mapping theorem, Closed graph theorem. Spectral theory, compact linear operators. | 7 (High Distinction) |
| 2005/06 | Summer Research - Algebraic Topology | Joe Grotowski | Rotman | Category theory, simplexes, homotopy, singular homology, exact sequences. Homotopy groups of spheres. | NA |
| 2006 Summer | AMSI Summer School - Permutation Group Theory | John Bamberg | Group Actions, transitive groups, primitive groups and the O'Nan-Scott Theorem. Semidirect product, wreath products. | 85 (High Distinction) | |
| 2006 Summer | AMSI Summer School - Computational Group Theory | Eamonn O'Brien | Permutation groups, base and strong generating sets. Finitely presented groups, coset enumeration. Polycyclic groups. Linear groups. Computations with Magma. | 80 (High Distinction) | |
| 2006/1 | MATH4303 - Advanced combinatorics | Peter Adams, Liz Billington, Darryn Bryant, Matt Dean, Dan Horsley | Ramsey theory, graph Ramsey theory. DNA sequencing. Graph decompositions. Cayley graphs and automorphism group of a graph. Combinatorial game theory. Combinatorial matchings. Project - Elliptic curve cryptography. | 7 (High Distinction) | |
| 2006/1 | MATH4402 - ODEs | Min-Chun Hong | Verhulst | IVP, existence by Banach contraction mapping. Gronwall's Inequality. Linear systems, Jordan form, linearisation. Lyapunov method. Periodic solutions, Morse Theorem, Poincare-Bendixson Theory. Periodic systems, Flocquet Theory, Brouwer fixed point theorem. | 7 (High Distinction) |
| 2006/1 | MATH6006 - Special Topics: Algebraic Methods of Quantum Physics | Jon Links | Review of Lie theory. O(4) symmetry of the hydrogen atom. Hopf algebras, quantum teleportation. Essay - Geometric algebra and the Dirac equation. | 7 (High Distinction) | |
| 2006/Year | MATH6010 - Thesis: Descent on elliptic curves | Victor Scharaschkin | Algebraic curves, elliptic curves. Hensel's Lemma and p-adic numbers. Group cohomology, Sha and Selmer groups. 2-descent. The Mordell-Weil theorem. | 7 (High Distinction) | |
| 2006/2 | MATH4304 - Number Theory | Victor Scharaschkin | Fermat's Last Theorem. Number fields. Integral closure, integral basis, norm, trace, discriminant, quadratic and cyclotomic fields. Decomposition of primes, Dirichlet unit theorem. The class group. Minkowski's bound and the geometry of numbers. Some algorithms for algebraic number theory. Continued Fractions. Chevalley-Warning Theorem, Hensel's Lemma, p-adic numbers. | 7 (High Distinction) | |
| 2006/2 | MATH4405 - Measure Theory | Bevan Thompson | Bartle | Lebesgue integral & measure. Monotone convergence. Fatou & Lebesgue dominated convergence theorems. Modes of convergence. Bounded variation. Absolute continuity. Signed measures. Generation of measures. Radon-Nikodym & Riesz representation theorems. Product measures. | 7 (High Distinction) |
| Fall 2007/Spring 2008 | MATH511A/B - Algebra | David Savitt | Knapp | Linear algebra, groups, rings, modules, Galois theory. | A |
| Fall 2007/Spring 2008 | MATH523A/B - Real Analysis | Leonid Friedlander | Folland | Set theory, measure theory and integration, Lp spaces, functional analysis, Fourier analysis. | A |
| Fall 2007/Spring 2008 | MATH534A/B - Topology/Geometry | Hermann Flaschka | Lee, Hatcher | Smooth manifolds, Stokes' theorem, some differential geometry. The fundamental group, homology, De Rham cohomology. | A |
| Fall 2008 | MATH519 - Topics course: Tate's Thesis | David Savitt | Ramakrishnan and Valenza | Topological groups, representation theory, Pontryagin duality, local and global fields, adeles and ideles, some class field theory, Tate's thesis. | A |
| Fall 2008 | MATH596G - RTG Project | Doug Ulmer | Lorenzini | The analogy between number fields and function fields. Ranks of quadratic twists of elliptic curves over F_q(T). | A |
| Fall 2008/Spring 2009 | MATH536A/B - Algebraic Geometry | Doug Ulmer | Shafarevich | Affine and projective varieties, morphisms and rational maps. Dimension, degree and smoothness. Basic coherent sheaf theory and Cech cohomology. Line bundles, Riemann-Roch theorem. | A |
| Spring 2009 | MATH518 - Topics course: Integral Lattices, Linear Codes and Finite Groups | Pham Tiep | Root lattices and lattice constructions using linear codes. Grothendieck group of integral lattices. Elkies theorem on long shadow lattices. Classification of unimodular lattices up to rank 24. Optimality of the Leech lattice. Weil representations. | A | |
| Spring 2009 | ECE637 - Channel Coding | William Ryan | Channels and capacity. Finite fields. Linear codes, cyclic codes, BCH codes, Reed-Solomon codes. LDPC codes. Convolutional codes. | A | |
| Fall 2009 | MATH577 - Topics Course: Information Theory | Marek Rychlik | MacKay | Bayesian probability, some information theory, data compression. | A |
| Fall 2009 | MATH563 - Probability Theory | Jan Wehr | Koralov and Sinai | Random variables, expectation and integration, Borel-Cantelli lemmas, independence, sums of independent random variables, strong law of large numbers, convergence in distribution, central limit theorem, infinitely divisible distributions. | A |
| Fall 2009/Spring 2010 | MATH520A/B - Complex Analysis | Tom Kennedy | Stein and Shakarchi | Analyticity, Cauchy's integral formula, residues, infinite products, conformal mapping, Dirichlet problem, Riemann mapping theorem. Riemann Surfaces. | A | Spring 2010/Fall 2010 | ECE535/537 - Digital Communications | Bane Vasic | Fundamentals of Iterative Decoding, Partial Response Channels, Constrained Coding, Construction of Low Density Parity Check codes, Non-binary LDPC codes, Linear Programming Decoding. | A |