B.Sc. Hons Applied Mathematics, with distinction and a 90% aggregate. Funding Harry Crossley Foundation Honours Research Fellowship
 UCT Council Senior Entrance Merit Scholarship
 Hyman Liberman Scholarship
The Hyman Liberman Scholarship is awarded in each year to the student with the highest overall B.Sc. results in the preceding year. CoursesThese courses were selected from the departments of Applied Mathematics, Physics, Statistics, Mechanical Engineering and Electrical Engineering. Advanced Mathematical Physics A  Existence and stability of soliton solutions Singular perturbation expansion Adiabatic approximations Topological solitons Vortices in ferromagnets GrobPitaevski, Maxwell and ChernSimons vortices Magnetic monopoles, instantons
 Advanced Mathematical Physics B  Inverse Scattering Transform for the nonlinear Schrodinger, KdV and sineGordon NLS as a Hamiltonian system Infinite sequences of integrals of motion The Riemann problem Applications to solitons of the principle of chiral fields Reduction group Applications to the twodimensional Toda lattices
 Continuum Mechanics  Tensor algebra and analysis Configurations and kinematics of continuous media Deformation and strain tensors Balance of mass, linear and angular momentum, and energy: the stress tensor Constitutive theory Linear elasticity Ideal fluids and Newtonian fluids Viscous Newtonian fluids and NavierStokes
 Quantum Mechanics  Hilbert spaces Schrodinger's Equation in coordinate and momentum space Uncertainty principle Linear harmonic oscillator by Dirac's method Rotation Groups Creation/annihilation operations Spin Timedependent
perturbation Radiative decays Gauge invariance Supersymmetry Pauli, Dirac and KleinGordon equations Relativistic corrections to the hydrogen atom Zeeman and Stark effects
 Operations Research A & B
 Linear progamming, the dual problem Integer programming Pareto frontiers Call center simulations Queue modelling Memoryless processes Exponential and Poisson distributions
 Decision Modelling  Decision trees Criteria weighting methods Quantifying preferences Utility curves Expected utility
 Nonlinear optimisation
 Optimisation problems Gradient descent Quadratic programming KarushKuhnTucker equations
 Digital Signal Processing  Digital Signal Processing Discrete Time Fourier Transform ZTransform Continuous time systems Converting discrete and continous time DFT and FFT Filter design Radar Signal Processing Analytic representation and sampling of signals Linear radar system model Transmit pulse waveforms Image Processing Multidimensional signal processing The human visual system Image formation in digital and optical systems Edge detection methods
 Electronic Circuits  Diode and Zener junctions and circuit analysis AC models of Bipolar Junction Transistors (BJT's) Tequivalence, EbersMoll model Basic follower, amplifier circuit configurations Commonemitter biasing Midpoint collector feedback Miller's theorem, feedback in amplifiers Transistor high frequency behaviour Differential amplifiers (longtailed pair) Darlington and cascode connections Wilson and other current mirrors
 Operational Amplifiers
 Frequency dependence and bode plots Slew rate, bias current, offset voltage Linear opamp circuits Optional inverter Inverting amplifier Follower with gain Universal addersubtractor Differential amplifiers and CMRR Transimpedance amplifier Opamp applications Integrators and (stable) differentiators FETswitched inverters and setable integrators Rectification and peak detection Hysteretic comparators and relaxation oscillators Synchronous detection Bootstrapping impedances Lab Project: Voltage Controlled Oscillator Filters sdomain analysis of opamp circuits Stabilisation with leadlag network Weinbridge oscillator and inductorless design Bessel, Chebyshev and Butterworth filters Sallen and Key filter realisation Multiple feedback bandpass filter State variable filter and notch filters

