im thinking of taking 4 courses+1 course on a p/f basis(so i could really slack off in that course). here are descriptions of various courses i might like to take, with my comments: fall: analysis1-A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line. *terrible teacher. probability-Basic combinatorial probability. Introductory distribution theory of univariate and multivariate distributions with special reference to the Binomial, Poisson, Gamma and Normal distributions. Characteristic functions. Weak law of large numbers. Central limit theorem. *prereq is analysis2 but i'll most definitely take it. pde-First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems. algebra3-Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains. *great teacher, but afraid the class is too hard for me. advanced materials-The physicochemical properties of advanced materials. Topics discussed include photonics, information storage, 'smart' materials, biomaterials, clean energy materials, porous materials, and polymers. qm1-Experimental basis for quantum mechanics; wave-packets; uncertainty principle. Hilbert space formalism. Schrodinger equation: eigenvalues and eigenvectors: applications to 1-d problems including the infinite and finite potential wells and the harmonic oscillator. Tunneling. Time independent perturbation theory. neurosciences1-An overview of cellular and molecular neuroscience at the graduate level. Topics include: synthesis, processing and intracellular transport of macromolecules; development of the nervous system including neurogenesis, axonal pathfinding, synaptogenesis and myelination; neuronal survival and response to injury; generation and propagation of action potentials; neurotransmitters and synaptic transmission. *this course has a term paper, and i would only take it if i decided against both pde and qm, and therefore planned to do research in pure biological sciences. but then the other math courses would also seem to be out of place. interm physiology1-In-depth presentation of experimental results and hypotheses on cellular communication in the nervous system and the endocrine system. winter: analysis2-Series of functions including power series. Riemann integration in one variable. Elementary functions. *same terrible teacher statistics-Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance. algebra4-Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals. *same good teacher, but the course is only harder. graph theory-Graph models. Graph connectivity, planarity and colouring.Extremal graph theory. Matroids. Enumerative combinatorics and listing. pde2-continuation of topics introduced in pde. optics-Geometrical optics, wave optics, lasers, Fourier transform spectroscopy, holography, optical data processing, stellar interferometry. qm2-Angular momentum and spin operators. Operator methods in quantum mechanics. Coupling of spin and angular momenta. Variational principles and elements of time dependent perturbation theory (the Golden Rule). Solution of the Schrodinger equation in three dimensions. Applications to the hydrogen and helium atoms and to simple problems in atomic and molecular physics. neuroscience2-An overview of the structure, function and interaction of neuronal systems of vertebrates. Topics include basic neuroanatomy, coding and processing of sensory information (somatic sensory, visual and auditory systems), control of posture and voluntary movement, learning and memory, processing of language and speech, cerebral blood flow, the neuroendocrine system and neuroimmunology.