## Course Descriptions

**First Year**- Physics 125-1 Mechanics
- Physics 125-2 Electricity and Magnetism
- Physics 125-3 Waves and Oscillations
- Math 281-1 Multidimensional Calculus
- Math 281-2 Vector Operators and Ordinary Differential Equations
- Math 281-3 Systems of Differential Equations, Linear Algebra and Infinite Series
- Chemistry 171-0 Advanced General Inorganic Chemistry
- Chemistry 172-0 Advanced General Physical Chemistry

**Second Year**- Math 381-0 Fourier Analysis and Boundary Value Problems for ISP
- Math 382-0 Complex Analysis and Group Theory for ISP
- Earth and Planetary Sciences 350 Physics of the Earth for ISP
- Chemistry 212-1 Organic Chemistry
- Chem 348-0 Physical Chemistry for ISP
- Biology 241 ISP Biochemistry
- Biology 240 Molecular and Cell Biology
- Physics 339-1 Quantum Mechanics
- Physics 339-2 Quantum Mechanics

**Third Year**

### First Year

##### Physics 125-1 Mechanics

- A. Vector kinematics, dynamics, free body problems, work-energy theorem, angular momentum, torque, conservation of energy and momentum, rigid body motion, rotating coordinate systems, central force fields and plane motion, two-body problems, gravity, Kepler's laws, harmonic motion.
- B. Laboratory in particle motions and dynamics, collisions, and oscillations.

##### Physics 125-2 Electricity and Magnetism

- A. Electrostatics, electric field, flux and Gauss' Law, electric potential, gradient of potential, divergence theorem, differential form of Gauss' Law, DC circuits and Kirchhoff's Laws, conductors, capacitors, RC circuits.
- B. Fields of moving charges, magnetic field, vector potential, Hall effect, electromagnetic induction, self-inductance, displacement current, Maxwell's equations, alternating current circuits, electric fields in matter, dipole distributions, polarizability tensor, polarized matter, electric susceptibility, dielectrics, magnetic fields in matter, field of a current loop, field of a permanent magnet, relativistic invariance and transformations.
- C. Laboratory in electrostatics, DC circuits, oscilloscope, e/m ratio of electron, RC circuits.

##### Physics 125-3 Waves and Oscillations

- A. Damped and driven oscillations, the superposition principle, coupled oscillators, resonance, traveling waves, refraction and dispersion, energy flux, reflection and transmission, wave packets, group velocity, waves in two and three dimensions, wave guides, polarization, geometrical optics, interference and diffraction, Huygen's principle, apertures and Fresnel integrals.
- B. Waves in solids and fluids, intro to materials physics, basic concepts of structure of matter from smallest to largest size scale.
- C. Concepts of quantum mechanics, Schrödinger equation, wave equation, particle in a box, particle waves in atoms.

##### Math 281-1 Multidimensional Calculus

- A. Vectors in 3-space, vector functions and their calculus, dot and cross products, lines, planes, line integrals.
- B. Graphing, quadric surfaces, functions of several variables, partial and directional derivatives, gradients, tangent planes, chain rule, cylindrical and spherical coordinates, double and triple integrals, improper integrals.
- C. Parametric surfaces, surface area, surface integrals, vector fields, conservative fields.

##### Math 281-2 Vector Operators and Ordinary Differential Equations

- A. Gauss', Green's, and Stokes' theorems, ordinary differential equations (exact, first order linear, second order linear), vector operators, existence and uniqueness theorems, graphical and numerical methods.
- B. Sequences and series, convergence tests, power series, Taylor series in one and several variables, error estimates, critical points, Lagrange multipliers.

##### Math 281-3 Systems of Differential Equations, Linear Algebra, and Infinite Series

- A. Series solutions of differential equations at regular singular points, Bessel's equation.
- B. Linear algebra: matrices, Gaussian elimination, rank, vector spaces, linear independence and bases.
- C. Linear systems of differential equations and related linear algebra: determinants, eigenvalues and eigenvectors, normal modes, principal axis theorem.
- D. Nonlinear systems.

##### Chemistry 171-0 Accelerated General Inorganic Chemistry

- A. Chemistry of solids, liquids and gases.
- B. Gas laws and stoichiometry.
- C. Chemical periodicity and atomic structure.
- D. Atoms, molecules, and continuous structures.
- E. Lewis theory of chemical bonding, valence bond and molecular orbital descriptions of bonding.
- F. Chemical processes in past, present and future technologies.

##### Chemistry 172-0 Accelerated General Physical Chemistry

- A. Chemical equilibrium.
- B. Acid-base equilibria.
- C. Dissolution and precipitation equilibria.
- D. Thermodynamic processes and thermochemistry.
- E. Spontaneous change and equilibrium.
- F. Electrochemistry.
- G. Chemical kinetics.
- H. How it all fits together: hemoglobin.

### Second Year

##### Math 381-0 Fourier Analysis and Boundary Value Problems for ISP

- A. Orthogonal functions, Sturm-Liouville theory, Fourier series, convergence in mean, Parseval theorem, heat equation, initial-BVP for Heat equation, numerical methods for heat equation.
- B. Fourier transforms, Fourier inversion formula and the normal density function, heat equation for the infinite rod, Gauss-Weierstrass convolution.
- C. Vibrating string, perturbed and struck string: initial-BVP for the finite string, infinite string, and d'Alambert's formula.
- D. Sturm-Liouville problems in two dimensions, vibrating membrane, cylindrical and spherical coordinates, Bessel functions, perturbed and struck Drumhead: Initial-BVP for the circular membrane.
- E. Steady-state (Laplace's equation) in rectangular, circular, and spherical geometry, Poisson integral representation theorem, Maximum principle, spherical harmonics and Legendre functions.

##### Math 382-0 Complex Analysis and Group Theory for ISP

A. Types of groups, symmetrical groups, matrix representations, homomorphisms and

isomorphisms, reducible and irreducible representations, oscillating particle problem.

B. Complex numbers and the complex plane, polar form and roots, complex functions and differentiation, Cauchy-Riemann equations and harmonic functions, Line integrals and the Cauchy-Goursat theorem, Analytic functions, Cauchy's theorem and Cauchy's formula, antiderivatives, Cauchy inequalities, Maximum modulus theorem, Laurent series and the residue theorem, isolated singularities, Residue theorem and application to evaluation of integrals.

C. Analytic functions as mappings, conformal mappings and linear fractional transformations, analytic and harmonic functions in applications, residue calculation of the Gauss-Weierstrass kernel, Harmonic functions as solutions to steady-state problems, finite groups and their matrix representations.

##### Earth and Planetary Sciences 350 Physics of the Earth for ISP

A. Basic facts about the Earth as a planet and the plate tectonics system, plate kinematics, composition of earth layers.

B. Gravitational attraction in the solar system, motion of planets and satellites, Kepler's laws, influence of rotation on the Earth's gravity field, shape of the Earth, evolution of the Earth-Moon system, gravity anomalies, isostasy.

C. Seismology, elementary continuum mechanics, strain and stress, waves in musical instruments: strings and winds, seismic waves: body waves, surface waves, normal modes, reflection and refraction of seismic waves, the case of a spherical Earth, seismic profiles inside the Earth, Adams-Williamson's model.

D. The Earth's magnetic field, principles of paleomagnetism, field reversals, simple models of dynamos, magnetic anomalies on the ocean floor, dating of oceanic lithosphere.

E. Heat transfer, radiation: greenhouse effect, conduction: Heat equation, simple models of the cooling of the oceanic lithosphere, Lord Kelvin's estimate of the age of the Earth, the failure of conductive models, convection: simple models.

F. Radiometric dating and geochemistry, elementary radioactive systems, radioactive dating: 14-C; 40-K; 87-Rb; the Pb series, initial ratios and reservoirs, mantle partitioning, Patterson's measurement of the age of the Earth.

##### Chemistry 212-1 Organic Chemistry

A. Basic concepts of organic chemistry including the structure and properties of organic molecules, acid-base reactions, SN1, SN2, E1, and E2 reactions, reaction mechanisms, condensed and line-angle structures.

B. Structure, naming, and stereochemistry of alkanes and cycloalkanes, chemical reactions of alkanes, conformational analysis, structure, synthesis and reactions of alkyl halides, alkenes and alcohols, nomenclature and stereochemistry of organic molecules,

chiral and achiral compounds, optical activity.

C. Laboratory: thin layer chromatography, distillations, extractions, filtrations, synthesis of organic compunds, JOC style lab reports.

##### Chemistry 348-0 Physical Chemistry for ISP

A. Work and heat, first, second, and third laws, bond energies, state functions, entropy, free energy functions.

B. Fundamental equations, Maxwell Relations, chemical potential, phase equilibrium, ideal mixtures, colligative properties, real mixtures, phase rule, phase diagrams, reaction equilibrium.

C. Statistical mechanics: postulates, distributions, canonical ensemble, partition and thermodynamic functions, heat capacities, equilibrium constants, elementary kinetics.

D. Reaction mechanisms, complex reactions, collision theory, activated complex theory, molecular reaction dynamics.

##### Biology 241 ISP Biochemistry

A. Cellular environments: polar and nonpolar interactions, hydrophobic driving force, properties of water.

B. Structure of proteins: primary, secondary, tertiary, quaternary, amino acid structures, motifs, domains, dynamics, and folding, Rasmol, structural/functional relationships, enzyme function and kinetics, biochemistry of active sites.

C. Nucleic acid structure/function, biological membranes: lipid and protein components, transport proteins.

D. Metabolic energy generation, glycolysis, gluconeogenesis, citric acid cycle, biological oxidation: electron and proton transport, energy coupling: ATP synthesis, energy capture: photosynthesis.

E. Lab: gel electrophoresis, SDS Polyacrylamide gel electrophoresis (proteins), DNA transformation, restriction enzyme mapping, Western-blots, chimeric proteins, yeast twohybrid assay, enzyme kinetics, recombinant DNA technology.

##### Biology 240 ISP Molecular and Cell Biology

A. Chromosomes, mitosis and meiosis, heredity and genetics, nucleic acids, recombinant

DNA technology, DNA replication and repair, transcription, translation, control of gene expression.

B. Membrane structure and transport, cells, protein sorting and transport, cell signaling, cytoskeleton, cell cycle control, cell division, tissues, cancer.

##### Physics 339-1 Quantum Mechanics

A. Need for a quantum theory, review of classical wave theory, introduction to quantum mechanics, Schrödinger’s equation, particle flux and number conservation.

B. Simple systems, one-dimensional systems, step potential, rectangular barrier, Dirac delta function, function barrier, particle in a box, introduction to the harmonic oscillator.

C. Formalism of quantum mechanics, operators and functions, commutation relations, observables and operators, physical postulates: correspondence principle and

complementarity principle, eigenfunctions and eigenvalues, Hermitian operators and observables, review of Fourier series and Fourier integrals, Dirac bracket notation, relation between classical and quantum mechanics, review of Lagrangian and

Hamiltonian formulation of classical mechanics: Poisson brackets, Heisenberg uncertainty principle, harmonic oscillator: ladder operators.

D. Systems of several particles, multiple particle wavefunctions, identical particles, permutation and exchange operators, fermions and bosons, Fermi and Bose statistics,

slater determinants.

E. Electrons in metals, free electron model, Born-von Karman boundary conditions,

Fermi sphere, thermodynamic properties of free electrons, electrons in a periodic potential: Bloch functions.

F. Angular momentum, general properties of angular momentum operators, commutation relations, eigenfunctions and eigenvalues of angular momentum operators.

##### Physics 339-2 Quantum Mechanics

A. Central force states and the hydrogen atom.

B. Spin, addition of angular momenta, time-independent perturbation theory for nondegenerate and degenerate states.

C. WKB approximation, scattering theory, and time-dependent perturbation theory.

### Third Year

##### Statistics 383-0 Probability and Statistics for ISP

A. Probability: Sample space, event and probability, combinations and permutations, conditional probability and Bayeh's theorem, independence and the binomial distribution.

B. Random variables: the distribution of a random variable, joint and conditional distributions, expectation and variance, propagation of error.

C. The Central Limit Theorem: Chebyshev's inequality and the law of large numbers, De

Moivre-Laplace and central limit theorems, Poisson distribution and Poisson approximation.

D. Interval estimation: Confidence intervals, chi-squared, F, and t distributions, confidence intervals for mu and sigma2.

E. Two-sample comparison: t-test, F test, comparison of two binomial proportions.

F. The method of maximum likelihood: method of moments and the MLE, score function, Fisher information, the Cramer-Rao inequality, asymptotic efficiency of the MLE.

G. Goodness-of-fit tests: parameters known and estimated, contingency tables, homogeneity and independence.

H. Regression: method of least squares, Gauss-Markov theorem, estimation in the linear model.

I. Correlation: Galton and "regression towards the mean”, bivariate normal distribution, estimation of the correlation coefficient.

##### Biology 310-0 ISP Quantitative Biochemistry and Molecular Biology

A. MWC model of hemoglobin saturation

B. Location of genetic markers on E. coli chromosome by random general transduction

C. Enzyme kinetics and its simplification

D. X-ray diffraction study of DNA fiber structure

E. Separable and non-separable (conventional) DNA supercoils

F. Variability plots to identify activity sites of proteins

G. DNA re-arrangement in the production of antibodies

H. 3-D structures of antibody-antigen complexes

I. TCR-MHC-peptide interaction and CD4

J. HIV and AIDS

##### Biology 311-0 ISP Neurobiology

A. Basic layout of the nervous system, neurons and glia, cell membranes, Nernst equation, Goldman-Hodgkin-Katz equation, equilibrium potentials.

B. Review of basic electricity and circuit theory, passive vs. active currents, neuronal membrane as circuit element, nonlinear current-voltage relations, the steady-state voltage equation, creation and maintenance of membrane potentials through ion channel activity.

C. Voltage clamp technique, Patch clamp technique.

D. The action potential: dissection into constituent ion carriers, sodium inactivation, action potential propagation through axon, gating charge and gating current, Hodgkin- Huxley model.

E. Different types of ion channels and neurotransmitters, metabotropic vs. ionotropic receptors, pharmacological agonists and antagonists, electrical synapse, chemical synapse, synaptic integration, transmitter release, neurons as electrical conductors.

F. Systems level neuroscience: Visual System

##### Physics 339-3 Particle and Nuclear Physics

A. Neutrons and protons: properties and interactions, Yukawa particle.

B. u and d quarks: baryons, mesons, decay modes.

C. Heavier quarks: particles and decays.

D. Weak interactions: standard model.

E. Deuteron: wave function, magnetic moment.

F. Complex nuclei: mass formula, shell model, other models.

G. Applied nuclear physics: fission, fusion, nuclear astrophysics.

##### Astronomy 331-0 Astrophysics

A. Introduction and survey of observations: distance scales, color brightness diagrams, luminosities, masses, time scales, stellar populations, star clusters.

B. Equations of stellar structure: hydrostatic equilibrium, estimates of interior conditions,

virial theorem.

C. Properties of matter: ideal gas law and radiation pressure, excitation, ionization,

Fermi-Dirac statistics and equation of state for degenerate matter; absorptive properties of matter: electron scattering, bound free absorption, free absorption.

D. Fundamental of radiation and convective energy transport.

E. Nuclear energy production: hydrogen burning: pp chain and CNO cycle, helium and heavy element burning; neutrino loss processes.

F. Simple stellar models: polytropes, Lane Emden equation, Eddington standard model, homologous Transformations.

G. Evolution: star formation, protostars, Hayashi phase, T Tauri stars, red giant branch, horizontal branch, variable stars, mass loss, asymptotic giant branch, planetary nebulae.

H. Final stages of evolution: nucleosynthesis, stellar collapse, white dwarf structures, white dwarf cooling, supernovae, neutron stars and black holes.

I. Binary stars: fundamentals of the Roche model, evolution.