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College Undergraduate Courses

Math | Biology | Chemistry | Anatomoy & Physiology
Psychology | Physics | Engineering

Undergraduate Math Courses

Functions and their graphs: polynomial, rational, exponential, logarithmic and trigonometric functions; conic sections; topics in trigonometry; graphical and analytical solutions of systems of equations and inequalities, trigonometric forms of a Complex number and DeMovire's Theorem; sequences and series.

Limits, continuity, and differentiation of algebraic functions. Applications of differentiation; exponential, logarithmic, and trigonometric functions and their derivatives; the definite integral and the fundamental theorem of calculus. Application of the integral. The Riemann sum, Intermediate Value Theorem, Mean Value Theorem, L'Hospital's rule and more.

Theoretical treatments and Applications of Definite Integrals. Techniques of Integration. Infinite sequences and series and convergence and divergence of series. Taylor Series and polynomial Approximations. Line integrals. Parametric equations and polar coordinates. Elementary differential equations. Basic proof methods.

Analytic geometry in three dimensions, vectors and vector functions, planes in three dimensions, chain rule, partial derivatives, and parametric equations. Gradient, delta-epsilon argument of limits of three variables. Continuity, differentiation, contour maps and level curves, equations to tangent planes and tangent vectors to a surface. Vector Analysis. Multiple integrals, line integrals, Lagrange multipliers and optimization questions. Cauchy-Schwartz inequality, The Triangle Inequality.

This course prepares students for advanced math courses. Attention is given to constructing and understanding proofs. Direct and indirect methods of proof, epsilon-delta arguments, method of mathematical induction.

The real numbers, sequences, limits, continuity, differentiation in one variable. Proof writing ideas and techniques. Delta-epsilon arguments [treatments] of limits, continuity, properties of derivatives and proofs of the properties, induction hypothesis, proving irrational numbers such as pi and root 2, transcendental numbers like e, Algebraic numbers, least upper bound. Supremum and Infimum approaches to Integral. Lower sums and upper sums of integrals. Proofs of Fundamental Theorem of Calculus I and II.

Series of numbers and functions, integration of functions of one variable, pointwise and uniform convergence, differential calculus in several variables, implicit and inverse function theorems. Taylor polynomial approximations. Homomorphism and Isomorphism. Fields.

A rigorous proof based approach of basic properties of Integers following from the division algorithm, primes and their distribution. Diophantine equations and elementary arithmetical functions. Congruences, continued fractions, sums of squares, quadratic residues, existence of primitive roots, arithmetic functions, quadratic reciprocity, transcendental numbers, Chinese remainder theorem, Fermat's little Theorem.

Advanced topics in Euclidean geometry and non-Euclidean geometry – spherical and hyperbolic geometry. Rigorous axiomatic development of systems including approach of Hilbert. And more topics including, lattice point geometry, projective geometry, and symmetry.

Vector spaces, systems of linear equations, matrices, Gaussian elimination, symmetric matrices, the adjoint of a matrix, the transpose of a matrix, determinant of a matrix, the inverse of a matrix. Cramer's rule. Inner product spaces, eigenvalues and eigenvectors. Systems of linear inequalities and systems of differential equations. Orthogonal projections and orthogonality, orthonormality and orthonormal basis as well as standard basis. Classical theorems of vector analysis [Green, Gauss and Stokes].

Abstract vector spaces and linear transformations, inner product spaces, diagonalization, and canonical forms. Systems of ordinary differential equations and numerical techniques.

An introduction to the concepts and principles of symbolic logic: valid and invalid argument, logical relations among sentences and their basis in structure features of those sentences, formal languages and their use in analyzing statements of ordinary discourse [especially the analysis of reasoning involving truth-functions and quantifiers], and systems for logical deduction.

Introduction to the theory of groups and rings.

Elements of Galois theory, advanced topics in ring theory and linear algebra, construction with ruler and compass.

First- and second-order ordinary differential equations; systems of ordinary differential equations, and inequalities. Lipschitz condition and uniqueness, properties of linear equations, linear independence, Wronskians, variation-of-constants formula, equations with constant coefficients and Laplace transforms, analytic coefficients, solutions in series, regular singular points, existence of theorem, theory of two-point value problem, and Green's functions.

Metric spaces and the topology of R^n. Compact sets, the geometry of Euclidean Spaces, limits and continuous mappings. Rigorous definitions of limits using filter bases. Heine-Borel Theorem, Bolzanno-Weirstrass Theorem. Partial differentiation. Vector valued functions, extrema, the inverse and implicit function theorems, and multiple integrals. Line integral and surface integrals, the theorems of Green, Gauss, and Stokes.

Integration, sequences, and series, uniform convergence, differentiation of functions of several variables, implicit and inverse function theorems, formula for change of variables.

Direct and iterative methods of solution of linear algebraic equations and eigenvalue problems. Topics include: numerical differentiation and quadrature for functions of a single variable, approximation by polynomials and piece-wise polynomial functions, approximate solutions of ordinary differential equations, and solutions of nonlinear equations.

Factorization in Dedekind domains, integers in a number field, prime factorization, basic properties of ramification, and local degree.

Sets, relations, and functions; partially ordered sets; cardinal numbers; Zorn's lemma, well-ordering, and the axiom of choice; metric space; and completeness, compactness, and separability.

Complex numbers, elementary functions and analytic functions of a complex variable, complex integration, power series, residues, and conformal mapping, Cauchy integral theory, series.

Metric and topological space, continuity, homeomorphisms, compactness, connectedness, homotopy, fundamental group.

Classification of second-order equations in two variables, wave motion and Fourier series, heat flow and Fourier integral, Laplace's equation and complex variables, second-order equations in more than two variables, Laplace operations, spherical harmonics, and associated special functions of mathematical physics.

Propositional and predicate logic and the syntactic notion of proof versus the semantic notion of truth [e.g. soundness and completeness]. Gödel completeness theorem, the compactness theorem and applications of compactness to algebraic problems.

The nature of mathematical knowledge and mathematical objects. The nature of proof and its demonstration.

Historical development of mathematical ideas in Eastern and Western cultures.



This widely-required course consists of studying measures of central tendency, measures of variability, normal and sampling distributions, student t distribution, chi squared distribution, confidence intervals, and hypothesis testing. Basic probability is often included as a separate unit.



Fundamentals and axioms; combinatorial probability; conditional probability and independence; binomial, poisson and normal distributions. Law of large numbers and the central limit theorem and random variables and generating functions.

Undergraduate Biology Courses

Life processes are studied to develop an understanding of structures and functions of organisms. Major topics are the cell theory, anatomy and adaptations of higher animals, interrelationships of man and the rest of the living world. Reproduction and development, classical and molecular genetics, evolution, behavior, and ecology are explored.

Introduction to the molecular and cellular levels of life. First semester traverses the cellular structure starting from the chemistry of life through the molecular workings of protein synthesis, arriving to the cellular organelle structure and function. The second semester focuses on plant and animal structure and function, both on the molecular and anatomical levels.

This course covers a detailed analysis of the biochemical mechanisms that control the maintenance, expression, and evolution of prokaryotic and eukaryotic genomes. The topics include gene regulation, DNA replication, genetic recombination, and mRNA translation. In particular, the logic of experimental design and data analysis is emphasized.

Detailed examination of the etiology, morphology, and physiology of pathogenic microorganisms as applicable to the hospital environment. The study of septic and aseptic techniques involving patients, equipment, and clinical areas enumerated.

Undergraduate Chemistry Course

Lecture and lab courses covering the atomic and molecular structure, the structuring of the periodic table, the concept of a mole, stochiometry, chemical bonding, properties of ideal gases, liquids, and solids. Also included are the chemistry of metals, the basis of electrical conductivity, chemical equilibrium, nuclear chemistry, radioactive decay, kinetics, redox reactions, and chemical equilibrium.

Lecture and lab courses starts building on the understanding of the atomic structure and bonding properties studied in general chemistry as applied to organic compounds. Using the reaction mechanism approach, electron transfer and the relationship between molecular structure and reactivity are explored. First semester focuses on the recognition and study of functional groups and the study of nomenclature. In the 2nd semester, there is a cursory examination of instrumental techniques, such as NMR and FTIR.

This course systematically survey the physical methods used in the investigation of biological systems, the models and underlying theory developed to account for observed behavior. The physical and chemical properties of amino acids, peptides, proteins, purines, pyrimidines, nucleic acids, and lipids will be examined from a spectroscopic, thermodynamic and kinetic viewpoint. Topics may include structure and function of biomolecules, metabolism (catabolism and anabolism), photosynthesis and recombinant DNA technologies. More specifically, this course may illustrate the basic principles through the biochemistry of contractile systems, active transport, drug metabolism, and neurochemistry.

Undergraduate Anatomoy and Physiology Courses

Overview of cell structure and function, tissue classification system, skeleton, muscular system, and nervous system.

Understanding of human nutrition requirements through the study of food groups, requirements to achieve a balanced diet, and the etiology of diseases stemming from improper nutrition. Often includes discussion topics on “hot-button” issues, such as alcohol consumption, trans-fat acid legislation, and the relationship between childhood allergies and attention deficit disorders.

Undergraduate Psychology Courses

Designed to familiarize the student with the science of the human behavior and mental states. Methods employed by psychologists, experimental findings and applications of research, and the study of learning are included. An introduction to the main theories of behavioral, psychoanalytic, neuroscientific, and cognitive schools of thought.

This course explores the development of children from birth to adolescence, in a wide range of areas including biological, cognitive, linguistic, social, and personality development. It also covers the effects of genes, experience, and social context on children's development.

Undergraduate Physics Courses

First of two introductory courses in general physics. One-dimensional motions. Vectors and two-dimensional motions. Newton's laws of motion. Conservation of energy and momentum. Rotational motions. Gravity. Statics and elasticity. Fluids. Oscillations. Heat and the laws of thermodynamics.

Second of two introductory courses in general physics. Electric forces and fields. Electric potential and capacitance. Electric current. Magnetic forces and fields. Faradays law and inductance. Maxwell's equations. Mechanical and electromagnetic waves. Geometrical optics. Interference and diffraction.

Electric forces and fields. Electric potential and capacitance. Electric current. Magnetic forces and fields. Faradays law and inductance. Maxwell's Theory of Electromagnetism. Electromagnetic waves. Light and Color. Geometrical optics. Image Formation. Interference and diffraction.

First of a two courses introductory sequence in general physics for majors other than science or engineering. One-dimensional motions. Vectors and Two- Dimensional Motions. Newton's Laws of motion. Conservation Laws of Energy and Momentum. Collisions. Rotational motions. Gravity. Statics and Elasticity. Fluids. Oscillations. Mechanical Waves. Superposition and Standing Waves. Sound and Acoustics.

Statics by virtual work and potential energy methods. Stability of equilibrium. Particle dynamics, harmonic oscillator and planetary motion. Rigid body dynamics in two and three dimensions. Lagrangian mechanics. Dynamics of oscillating systems.

Properties of the electrostatic, Magneto Static and Electromagnetic Field in vacuum and in Material media. Maxwell's Equations with applications to elementary problems.

(Courses are covered with an Engineering point of View) Straight line motion, velocity, speed, acceleration; Vectors; Motion in two and three dimensions; Force and Motion: Newton's laws, Friction, Circular Motion; Kinetic Energy and Work; Potential Energy and Conservation of Energy; Systems of Particles; Center of Mass, Conservation Laws; Elastic and Inelastic Collisions; Rotation, Torque, Angular Momentum; Rolling, Torque and Angular Momentum; Oscillations, Harmonic Motion, Pendulum, Damped and Forced Oscillations; Transverse and Longitudinal Waves, Interference, Sound.

Electric Charge and Coulomb's law; Electric Fields, Gauss's law; Electric Potential; Capacitance; Current and Resistance; Circuits; Magnetic Fields; Magnetic Fields due to Currents, Ampere's law; Induction and Inductance, Faraday's and Lenz's law; Magnetism of matter, Maxwell's Equations; Electromagnetic oscillations and Alternating current; Electromagnetic waves.

Images, Mirrors, and Lenses; Interference; Diffraction; Relativity; Photons and the Photoelectric effect; Matter waves; Atoms; Electricity in Solids, Semiconductors; Nuclear Physics, Radioactivity, Alpha and Beta decays; Fission and Fusion.

Engineering Course Description

Fundamentals of Electrical Circuits I

Passive DC circuit elements; Kirchhoff’s laws; Electric Power calculations; Analysis of DC circuits, Nodal and Loop analysis techniques; Voltage and current division, Thevenin’s and Norton’s theorems; Source free and forced responses of RL, RC and RLC circuits.

Fundamentals of Electrical Circuits II

Sinusoidal Steady-State response; Complex voltage and current and the Phasor concept, Impedance, Admittance; Average, apparent and reactive Power; Poly-Phase circuits; Node and mesh analysis for AC circuits; Use of MATLAB for solving circuit equations; Frequency response; Parallel and Series Resonance; Operational Amplifier circuits.

Fundamentals of Electronics I

Circuit models and frequency response of amplifiers; Op-amps, difference amplifier, voltage-to-current converter, slew rate, full-power bandwidth, common-mode rejection, frequency response of closed loop amplifier, gain-bandwidth product rule; Diodes, limiters, clamps, semiconductor physics; Bipolar Junction Transistors, small-signal models, cut-off, saturation and active regions, common emitter, common base, and emitter follower amplifier configurations; Field-Effect Transistors (MOSFET and JFET), biasing, small-signal models, common-source and common-gate amplifiers, integrated-circuit MOS amplifiers.

Fundamentals of Electronics II

Differential and Multistage Amplifier, Current Mirrors, Current Sources, Active loads; Frequency response of MOSFET, JFET and BJT amplifiers: Bode plots; Feedback amplifiers, Gain-Bandwidth rule, effect of feedback on frequency response; Class A, B, and AB output stages; Op-amp analog integrated circuits; Piecewise-Linear Transient Response; Determination of State of Transistors; Wave shaping circuits; MOS and bipolar digital design: Noise margin, fan-out, propagation delay; CMOS, TTL, ECL.

Signals and Systems

Linear System Theory for Analog and Digital systems; Linearity, Causality, Time Invariance. Impulse response, Convolution, Stability; The Laplace and Z - transforms and applications to Linear Time Invariant (LTI) systems; Frequency response, Analog and Digital Filter design; Fourier Series, Fourier Transforms, the Sampling Theorem.

Feedback Control Systems

Introduction to Analysis and Design of Linear Feedback Control systems; Modeling of Physical Systems, Performance Specifications, Sensitivity and Steady-State error, Routh-Hurwitz and Nyquist Stability tests; The use of Root Locus and Frequency-Response techniques to analyze system performance, and design compensation (lead/lag and PID controllers) to meet performance specifications.

Electro-Magnetic Waves

Electromagnetic Wave Propagation in free space and in Dielectrics is studied starting from a consideration of distributed Inductance and Capacitance on Transmission lines; Electromagnetic Plane Waves are obtained as a special case; Reflection and Transmission at Discontinuities is discussed for pulsed sources, while impedance transformation and matching are presented for harmonic time dependence; Snell`s law and the Reflection and Transmission Coefficients at dielectric interfaces are derived for obliquely propagation plane waves; Guiding of waves by dielectrics and by metal waveguides is demonstrated.

Introduction to Programming

An Introduction to Computer Programming and problem solving; General topics covered include the fundamentals of programming, good software development practices and solving problems using computer programming; Specific topics include compiling, running and debugging a program, program testing, documentation, variables and data types, assignments, arithmetic expressions, input and output, top-down design and procedures, the random number generator, conditionals and loops functions, arrays, and an introduction to classes and object oriented programming.

Digital Logic and State Machine Design

Combinational and Sequential digital circuits; An Introduction to Digital systems; Number Systems and Binary Arithmetic; Switching Algebra and Logic design; Error Detection and Correction; Combinational integrated circuits, including adders; Timing hazards; Sequential circuits, flip-flops, state diagrams and synchronous machine synthesis; Programmable Logic Devices, PLA, PAL and FPGA; Finite state machine design; Memory elements.

Dynamics

Three-Dimensional treatment of the Kinematics of particles and rigid bodies using various coordinate systems; Newton's laws, Work, Energy, Impulse, Momentum, Conservative Force Fields, Impact; Rotation and Plane motion of Rigid Bodies.



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