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Principal Course Distribution Requirement

Principal courses offer introductions to the breadth of disciplines in the College. They acquaint students with the subject matter in an area, with the types of questions that are asked about that subject matter, with the knowledge that has been developed and is now basic to the area, and with the methods and standards by which claims to truth are judged.

Students must complete courses in topical groups in three major divisions (humanities, natural sciences and mathematics, and social sciences). For the B.A., three courses are required from each division, with no more than one course from any topical group. The B.G.S. requires two courses from each division, with no more than one from any topical group. To fulfill the requirement, a course must be designated as a principal course according to the codes listed below.

These are the major divisions, their topical subgroups, and the codes that identify them:

Humanities

  • HT: Historical studies
  • HL: Literature and the arts
  • HR: Philosophy and religion

Natural Sciences and Mathematics

  • NB: Biological sciences
  • NE: Earth sciences
  • NM: Mathematical sciences
  • NP: Physical science

Social Sciences

  • SC: Culture and society
  • SI: Individual behavior
  • SF: Public affairs

No course may fulfill both a principal course distribution requirement and a non-Western culture or second-level mathematics course requirement. Laboratory science courses designated as principal courses may fulfill both the laboratory science requirement and one of the distribution requirements. No free-standing laboratory course may by itself fulfill either the laboratory science requirement or a principal course requirement. Students should begin taking principal courses early in their academic careers. An honors equivalent of a principal course may fulfill a principal course requirement.

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Non-Western Culture Requirement

A non-Western culture course acquaints students with the culture, society, and values of a non-Western people, for example, from Asia, the Pacific Islands, the Middle East, or Africa. Students must complete one approved non-Western culture course.

One approved non-Western culture course is required. Occasionally courses with varying topics fulfill the non-Western culture course requirement. See the Schedule of Classes for details. These courses are coded NW.

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Transfer and Earned Credit Course Codes

These codes are used to evaluate transfer credit and to determine which academic requirements a course meets.

  • H: Humanities
  • N: Natural Sciences and Mathematics
  • S: Social Sciences
  • W: World Civilization and Culture
  • U: Undesignated Elective Credit (course does not satisfy distribution requirement)
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An introduction to the mathematical methods of deterministic control theory is given by considering some specific examples and the general theory. The methods include dynamic programming, the calculus of variations, and Pontryagin's maximum principle. Various problems of linear control systems, e.g., the linear regulator problem, are solved. Prerequisite: MATH 320 or equivalent. LEC
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Divisibility, the theory of congruences, primitive roots and indices, the quadratic reciprocity law, arithmetical functions and miscellaneous additional topics. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC
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Stochastic adaptive control methods. Stochastic processes such as Markov chains and Brownian motion, stochastic integral, differential rule, stochastic differential equations, martingales and estimation techniques. Identification and control of discrete and continuous time linear stochastic systems. Specific applications and simulation results of stochastic adaptive control theory. Prerequisite: MATH 627 and some knowledge of control. LEC
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MATH 765 and MATH 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; derivatives and integrals of functions of one and of several real variables. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC
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A continuation of MATH 765. Prerequisite: MATH 765. LEC
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Computational aspects of linear algebra, linear equations and matrices, direct and indirect methods, eigenvalues and eigenvectors of matrices, error analysis. Prerequisite: MATH 590 and MATH 781. LEC
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Finite and divided differences. Interpolation, numerical differentiation, and integration. Gaussian quadrature. Numerical integration of ordinary differential equations. Curve fitting. (Same as EECS 781.) Prerequisite: MATH 320 and knowledge of a programming language. LEC
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Direct and iterative methods for solving systems of linear equations. Numerical solution of partial differential equations. Numerical determination of eigenvectors and eigenvalues. Solution of nonlinear equations. (Same as EECS 782.) Prerequisite: MATH 781. LEC
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Finite difference methods applied to particular initial-value problems (both parabolic and hyperbolic), to illustrate the concepts of convergence and stability and to provide a background for treating more complicated problems arising in engineering and physics. Finite difference methods for elliptic boundary-value problems, with a discussion of convergence and methods for solving the resulting algebraic system. Variational methods for elliptic problems. Prerequisite: MATH 647 or equivalent. LEC
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A theoretical course on the fundamental concepts and theorems of linear algebra. Topics covered are: vector space, basis, dimension, subspace, norm, inner product, Banach space, Hilbert space, orthonormal basis, positive definite matrix, minimal polynomial, diagonalization and other canonical forms, Cayley-Hamilton, spectral radius, dual space, quotient space. Prerequisite: MATH 590. LEC
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This course includes the following topics: multiplicative properties of the integers and introductions to group theory, ring theory and field theory. Prerequisite: MATH 223 and MATH 290, or equivalent. LEC
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Arranged as needed to present appropriate material for groups of students. May be repeated for credit. Prerequisite: Variable. LEC
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Directed readings on a topic chosen by the student with the advice of an instructor. May be repeated for additional credit. Consent of the department required for enrollment. RSH
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Cauchy's theorem and contour integration; the argument principle; maximum modulus principle; Schwarz symmetry principle; analytic continuation; monodromy theorem; applications to the gamma function and Riemann's zeta function; entire and meromorphic functions; conformal mapping; Riemann mapping theorem; univalent functions. Prerequisite: MATH 766 or concurrently with MATH 766. LEC
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Continuation of MATH 800. Prerequisite: MATH 800. LEC
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Axiomatic set theory; transfinite induction; regularity and choice; ordinal and cardinal arithmetic; miscellaneous additional topics (e.g., extra axioms such as GCH or MA; infinite combinatorics; large cardinals). Prerequisite: MATH 765 or MATH 791, or concurrent enrollment in MATH 765 or MATH 791, or equivalent evidence of mathematical maturity. LEC
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Measurable spaces and functions. Measure spaces and integration. Extensions of set functions, outer measures, Lebesgue measure. Signed and complex measures. Differentiation of set functions. Miscellaneous additional topics and applications. Prerequisite: MATH 766. LEC
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Continuation of MATH 810. Prerequisite: MATH 810. LEC
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General topology. Set theory; topological spaces; connected sets; continuous functions; generalized convergence; product and quotient spaces; embedding in cubes; metric spaces and metrization; compact spaces; function spaces. Prerequisite: MATH 765. LEC
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The fundamental group and covering spaces (including classification); compact surfaces; homology theory, computations (including homotopy invariance) and applications (including Brouwer fixed point theorem); introduction to cohomology theory. Prerequisite: MATH 790 and MATH 791 and MATH 820, or permission of instructor. LEC
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Review of simplicial homology; Lefschetz fixed point theorem and degree theory; singular, cellular, and axiomatic homology; Jordan Brouwer separation theorems; universal coefficient theorems, products in cohomology, homotopy groups, and the Hurewicz Theorem. Prerequisite: MATH 821. LEC
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An introduction to the fundamental structures and methods of modern algebraic combinatorics. Topics include partially ordered sets and lattices, matroids, simplicial complexes, polytopes, hyperplane arrangements, partitions and tableaux, and symmetric functions. Prerequisite: MATH 724 and MATH 791, or permission of the instructor. LEC
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A study of some structures, theorems, and techniques in algebra whose use has become common in many branches of mathematics. Prerequisite: MATH 790 and MATH 791. LEC
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Continuation of MATH 830. Prerequisite: MATH 830. LEC
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Multilinear algebra of finite dimensional vector spaces over fields; differentiable structures and tangent and tensor bundles; differentiable mappings and differentials; exterior differential forms; curves and surfaces as differentiable manifolds; affine connections and covariant differentiation; Riemannian manifolds. Prerequisite: MATH 765 and MATH 790. LEC
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Discrete and differentiable dynamical systems with an emphasis on the qualitative theory. Topics to be covered include review of linear systems, existence and uniqueness theorems, flows and discrete dynamical systems, linearization (Hartman-Grobman theorem), stable and unstable manifolds, Poincare sections, normal forms, Hamiltonian systems, and an introduction to bifurcation theory and chaos. Prerequisite: MATH 320 and MATH 766, or permission of instructor. LEC
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Topics to be covered include complex dynamical systems, perturbation theory, nonlinear analysis of time series, chaotic dynamical systems, and numerical methods as dynamical systems. This course may be repeated for credit. Prerequisite: MATH 850 or permission of instructor. LEC
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Markov chains; Markov processes; diffusion processes; stationary processes. Emphasis is placed on applications: random walks; branching theory; Brownian motion; Poisson process; birth and death processes. Prerequisite: MATH 627 and MATH 765. LEC
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This is a second course in stochastic processes, focused on stochastic calculus with respect to a large class of semi-martingales and its applications to topics selected from classical analysis (linear PDE), finance, engineering, and statistics. The course will start with basic properties of martingales and random walks and then develop into the core program on Ito's stochastic calculus and stochastic differential equations. These techniques provide useful and important tools and models in many pure and applied areas. Prerequisite: MATH 727 and MATH 865. LEC
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The general linear hypothesis with fixed effects; the Gauss-Markov theorem, confidence ellipsoids, and tests under normal theory; multiple comparisons and the effect of departures from the underlying assumptions; analysis of variance for various experimental designs and analysis of covariance. Prerequisite: MATH 628 or MATH 728, and either MATH 590 or MATH 790. LEC
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The multivariate normal distribution; tests of hypotheses on means and covariance matrices; estimation; correlation; multivariate analysis of variance; principal components; canonical correlation. Prerequisite: MATH 628 or MATH 728, and either MATH 590 or MATH 790. LEC
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Game theory, admissible decision functions and complete class theorems; Bayes and minimax solutions; sufficiency; invariance; multiple decision problems; sequential decision problems. Prerequisite: MATH 628 and MATH 766. LEC
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Advanced topics in numerical linear algebra including pseudo-spectra, rounding error analysis and perturbation theory, numerical methods for problems with special structure, and numerical methods for large scale problems. Prerequisite: Math 781, 782, 790, or permission of the instructor. LEC
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Advanced course in the numerical solution of ordinary and partial differential equations including modern numerical methods and the associated analysis. Prerequisite: MATH 781, 782, 783, or permission of the instructor. LEC
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Introduction to modern techniques in Fourier Analysis in the Euclidean setting with emphasis in the study of functions spaces and operators acting on them. Topics may vary from year to year and include, among others, distribution theory, Sobolev spaces, estimates for fractional integrals and fractional derivatives, wavelets, and some elements of Caldern-Zygmund theory. Applications in other areas of mathematics, in particular partial differential equations and signal analysis, will be presented based on the instructor's and the students' interests. Prerequisite: Math 810 and Math 800, or instructor's permission. LEC
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Holomorphic functions in several complex variables, Cauchy's integral for poly-discs, multivariable Taylor series, maximum modulus theorem. Further topics may include: removable singularities, extension theorems, Cauchy-Riemann operator, domains of holomorphy, special domains and algebraic properties of rings of analytic functions. Prerequisite: MATH 800. LEC
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Algebraic sets, varieties, plane curves, morphisms and rational maps, resolution of singularities, Reimann-Roch theorem. Prerequisite: MATH 790 and MATH 791. LEC
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Injective and projective resolutions, homological dimension, chain complexes and derived functors (including Tor and Ext). Prerequisite: MATH 830 and MATH 831, or consent of instructor. LEC
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General properties of Lie groups, closed subgroups, one-parameter subgroups, homogeneous spaces, Lie bracket, Lie algebras, exponential map, structure of semi-simple Lie algebras, invariant forms, Maurer-Cartan equation, covering groups, spinor groups. Prerequisite: MATH 766 and MATH 790 and MATH 791. LEC
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Paracompact spaces, uniform spaces, topology of continua, Peano spaces, Hahn-Mazurkiewicz theorem, dimension theory, and theory of retracts. Prerequisite: MATH 820. LEC
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Probability measures, random variables, distribution functions, characteristic functions, types of convergence, central limit theorem. Laws of large numbers and other limit theorems. Conditional probability, Markov processes, and other topics in the theory of stochastic processes. Prerequisite: MATH 811. LEC
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Introduction; equations of mathematical physics; classification of linear equations and systems. Existence and uniqueness problems for elliptic, parabolic, and hyperbolic equations. Eigenvalue problems for elliptic operators; numerical methods. Prerequisite: MATH 766. LEC
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Topological vector spaces, Banach spaces, basic principles of functional analysis. Weak and weak-topologies, operators and adjoints. Hilbert spaces, elements of spectral theory. Locally convex spaces. Duality and related topics. Applications. Prerequisite: MATH 810 and MATH 820 or concurrent with MATH 820. LEC
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Continuation of MATH 960. LEC
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The basics of C*-algebras, approximately finite dimensional C*-algebras, irrational rotation algebras, C*-algebras of isometries, group C*-algebras, crossed products C*-algebras, extensions of C*-algebras and the BDF theory. Prerequisite: MATH 811 or MATH 960, or consent of instructor. LEC
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K0 for rings, spectral theory in Banach algebras, K1 for Banach algebras, Bott periodicity and six-term cyclic exact sequence. Prerequisite: MATH 790 and MATH 791 and MATH 960. LEC
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Advanced courses on special topics; given as need arises. Prerequisite: Variable. LEC
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A study of the art, science, concepts, and evolution of warfare as one instrument of political action throughout history. The study of selected battles and campaigns serves as a vehicle to emphasize the application of the classical principles of warfare, the influence of leadership, and the advancement of technology of the art and science of war. This course is substituted for NAVY 300 by NROTC students selected for Marine Corps training. Approved for degree credit in the College of Liberal Arts and Sciences effective fall 1975. Such courses count within the limit of twenty-five hours accepted from other schools and divisions. LEC
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An historical survey and evaluation of the concept, doctrinal origins, evolution, and strategic role of the amphibious projection of seapower ashore from antiquity and into the 20th century. The student studies and critiques historically significant amphibious campaigns. The student then evaluates the current and future need of an amphibious capability within the U.S. defense community. Approved for degree credit in the College of Liberal Arts and Sciences effective Fall 1976. Such courses count within the limit of 25 hours accepted from other schools and divisions. LEC
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A study of the biochemical principles of macromolecular structure and function, molecular communication, and the metabolism of nutrients and xenobiotics as applied to problems of medicinal and pharmacological significance. Prerequisite: Concurrent enrollment in MDCM 602 Lab. LEC
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Laboratory exercises illustrating the application of chemical principles to biochemical processes of medicinal, pharmacological, and clinical significance. Prerequisite: Concurrent enrollment in MDCM 601. LAB
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A study of the biochemical principles of macromolecular structure and function, biosynthesis, molecular communication, and the metabolism of nutrients and xenobiotics as applied to problems of medicinal and pharmacological significance. Prerequisite: MDCM 601. LEC
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This course will cover indigenous wisdom, ethnobotany, natural products chemistry and biotechnology to detail discoveries that are producing safe and effective medicines. The student will get familiarized with pharmacologically active compounds that were discovered from animals (frogs, leeches, insects, snakes); plants (terrestrial and marine); microorganisms (fungi and bacteria) as well as marine organisms. Prerequisite: MDCM 626 or instructor permission. LEC
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The course will provide a technical background for understanding the scientific basis underlying the use of herbal medicines. This will be followed by practical information about the pharmacological and chemical properties as well as clinical uses of herbal medicines. Active student participation in discussing the properties of these non-prescription medicinals is expected. Prerequisite: MDCM 601. LEC
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A study, from the molecular viewpoint, of the organic substances used as medicinal agents, including consideration of their origins, chemical properties, structure-activity relationships, metabolism and mechanisms of action; this course emphasizes drugs affecting the central nervous system. Prerequisite: CHEM 626 and MDCM 601. LEC
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A continuation of MDCM 625 with emphasis on autonomic and cardiovascular agents and peripherally-acting hormones. Prerequisite: MDCM 625. LEC
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A continuation of MDCM 625 and MDCM 626 with special emphasis on vitamins and anticancer, antiviral, antibacterial, and antifungal agents. Prerequisite: MDCM 625. LEC
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A discussion of the principles of contemporary drug design with specific examples chosen from the original literature. Prodrugs: bioisosteres; modulation of drug absorption, distribution, metabolism, and excretion; molecular dissection; rigid analogs; pharmacophores; etc., will be treated. Prerequisite: MDCM 627. LEC
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Research in medicinal chemistry. Students will be assigned to a laboratory research problem. Prerequisite: Consent of instructor. IND
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A lecture course designed to acquaint beginning research students with basic laboratory techniques, principles of laboratory safety, use of instrumental methods for structure elucidation, and the writing of scientific reports. Prerequisite: Consent of instructor. LEC
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This course encompasses original work on a laboratory problem of limited scope, honors reading assignments from medicinal chemistry literature, or in-depth discussions of assigned topics. Prerequisite: Consent of instructor. IND
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A study of the principles of macromolecular structure and function, biosignaling, bioenergetics and metabolism, with an emphasis on the relationship between biochemistry and medicine. Prerequisite: Graduate standing or permission of instructor. LEC
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A study of the principles of basic enzymology, including chemical reactions, biosynthesis, and metabolism. In addition, the course will cover lipids, hormones, vitamins, and minerals. Prerequisite: Graduate standing or permission of instructor. LEC
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The goal of this one-credit-hour course is to provide an overview of physiological mechanisms and disease processes as a background for intermediate level courses in medicinal chemistry, drug discovery and drug development. Prerequisite: One college-level course in biology. LEC
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An overview of the field of medicinal chemistry, including discussions of research techniques and the application of organic chemistry to medicinal chemistry problems. Prerequisite: Graduate standing or permission of instructor. LEC
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The discovery and properties of pharmaceutical agents, including a survey of the various drug classes important in clinical applications. The relationship between chemical structure and biological mechanism of action will be emphasized. Prerequisite: Graduate standing or permission of instructor. LEC
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A study, from the molecular viewpoint, of the organic substances used as medicinal agents, including consideration of their origins, chemical properties, structure-activity relationships, metabolism and mechanisms of action; this course emphasizes drugs affecting the central nervous system. Prerequisite: CHEM 626 and MDCM 621. LEC
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A continuation of MDCM 725 with emphasis on autonomic and cardiovascular agents and peripherally-acting hormones. Prerequisite: MDCM 725. LEC
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A continuation of MDCM 725 and MDCM 726 with special emphasis on vitamins and anticancer, antiviral, antibacterial, and antifungal agents. Prerequisite: MDCM 725. LEC
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Experimental approaches to understanding mechanism of drug action. Use of drugs as tools to understand functioning of biological systems will also be stressed. Historically important experiments will be discussed along with experiments which are currently used to define drug mechanisms. Topics will include: dose-response, drug receptors, drug metabolism, chemotherapy as well as autonomic CNS, cardiovascular and renal pharmacology. (Same as P&TX 742.) Prerequisite: BIOL 600 and BIOL 646 or equivalent, or consent of instructor. LEC
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An introductory graduate level course in bioorganic and medicinal chemistry, in which the principles of organic reaction mechanisms in biological systems are discussed. This course discusses the organic chemistry of metabolic transformations of biomolecules and their associated cofactors, both organic coenzymes and metal ions. LEC
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A detailed study of the molecular aspects of nerve transmission will be covered with special emphasis on the uptake, storage, release, biosynthesis, and metabolism of specific neurotransmitters. Drugs affecting these processes and current research on receptor isolation and receptor mechanisms will be discussed from a chemical viewpoint. (Same as BIOL 775, CHEM 775, NURO 775, P&TX 775, and PHCH 775.) Prerequisite: Consent of instructor. LEC
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A laboratory course designed to acquaint advanced undergraduate and beginning graduate students with laboratory safety, the research notebook, use of advanced instrumental techniques for structural assignment and verification, methods of separation and purification, and the use of advanced reagents and laboratory transformations relevant to research in medicinal chemistry. Prerequisite: Consent of instructor. LAB
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A discussion of bioassay-directed screening, the isolation, structure determination, biosynthesis, partial synthesis and total chemical synthesis of organic natural products of medicinal significance. Examples of the classes of compounds to be considered include steroid hormones, cardiac glycosides, alkaloids, antibiotics, terpenes, and the like. Prerequisite: Graduate standing or consent of instructor. LEC
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A discussion of the principles of contemporary drug design with specific examples chosen from the original literature. Prodrugs; bioisosteres; Kcat inhibitors; active site directed reversible and irreversible inhibitors; quantitative SAR; modulation of drug absorption, distribution, metabolism and excretion; molecular dissection; rigid analogs; pharmacophores; etc., will be treated. Prerequisite: Graduate standing or completion of MDCM 624 and MDCM 627. LEC
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An introduction to the chemical and biochemical principles which govern the interaction of drugs and chemicals with cells and organisms. Topics include absorption, distribution, metabolism, and excretion; passive vs. active processes; pharmacokinetics; bioactivation vs. detoxication; and applications in drug design and improvement. Prerequisite: One year of organic chemistry and one course in biochemistry. LEC
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A discussion of the principles of contemporary drug design with specific examples chosen from the original literature. Drug-like properties; conformational constraint; structure-based drug design; library generation; HTS hit optimization, will be treated. LEC
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Reports by research students and discussions of developments in the field not covered in formal courses. LEC
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Lectures and discussion on ethical issues in the conduct of a scientific career, with emphasis in the conduct of a scientific career, with emphasis on practical topics of special importance in molecular-level research in the chemical, biological, and pharmaceutical sciences. Topics will include the nature of ethics, the scientists in the laboratory, the scientist as author, grantee, reviewer, employer/employee, teacher, student, and citizen. Discussions will focus on case histories. Graded on a satisfactory/unsatisfactory basis. (Same as MDCM 801, NURO 801, P&TX 801, PHCH 801 and PHCH 802.) LEC
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The course will cover basic techniques of moral reasoning, especially as applied to ethical issues in the physical sciences and engineering. Topics covered will include the ethical conduct of research, the federal and professional guidelines for different kinds of research, and the ethical dimensions of publication and professional life. Emphasis will be on practical applications, cases and student involvement. (Same as GS 804, NURO 804, P&TX 804, and PHCH 804.) Prerequisite: Must be admitted to the program or division of Pharmacy to enroll in this class. LEC
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An in-depth examination of the pathways, enzymes, and mechanisms of xenobiotic biotransformation in a combined lecture-readings-discussion format. Emphasis will be on recent as well as classic methods of findings. Prerequisite: MDCM 790 or MDCM 791 or consent of instructor. LEC
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A laboratory course exemplifying various techniques used in studying the metabolism of foreign organic compounds in mammalian systems. In addition, enzymatic reactions in other plant and microbial systems are studied. Prerequisite: Consent of instructor. LAB
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Hours and credit to be arranged. RSH
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Hours and credit to be arranged. Independent investigation of a research problem of limited scope. Prerequisite: Consent of instructor. THE
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An in-depth discussion of topics of current interest to medicinal chemists. Prerequisite: Consent of instructor. LEC
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Theory and practice of contemporary molecular modeling: real-time computer graphics, model-building routines, use of structural databases, molecular mechanics and molecular dynamics calculations. The laboratory section places emphasis on drug design; work on own problems is welcome. (Same as BIOL 952.) Prerequisite: Graduate standing or consent of instructor. LAB
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Preparation of an original research proposal concerning contemporary problems in medicinal chemistry. Prerequisite: Consent of instructor. LAB
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Advanced level research in collaboration with a faculty member, which may involve projects in one or more of the following areas: organic synthesis, isolation and structure elucidation, metabolism, biochemical mechanisms of drug action. Prerequisite: Doctoral degree or equivalent in an appropriate related area, and consent of instructor. RSH
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Hours and credit to be arranged. Original chemical research in the synthesis and development of medicinal agents, elucidation of the chemical mechanisms of drug action, drug metabolism, and drug toxicities. THE
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The principles of statics, with particular attention to engineering applications. Prerequisite: PHSX 211. LEC
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Digital computing methods for solving mechanical engineering problems utilizing current programming languages and commercial software. Co-requisite: MATH 116 or MATH 121. LEC
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Introduction to graphics programs, introduction to computer aided design, familiarization with computer graphics hardware and software. LEC
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An introductory course on materials. Emphasis is placed on structure and the relation of structure to the behavior and properties of engineering materials. Prerequisite: CHEM 150 or CHEM 184 or consent of instructor. LEC
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Laboratory to supplement lecture on engineering materials properties and selection, manufacturing processes, and design for manufacturing. Prerequisite: CHEM 150 or CHEM 184. Corequisite: ME 306 and ME 311. LAB
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A basic treatment of stress and deformation in elastic bodies. Prerequisite: ME 201 and MATH 220. LEC
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