Course Descriptions - Department of Basic Sciences

	University Homepage \| Faculty of Science \| Email Login \|
	DEPARTMENT OF BASIC SCIENCES PHILADELPHIA UNIVERSITY

100 level

210101 Calculus I An introduction to analytic geometry, differentiation of algebraic and transcendental functions, applications of differentiation, and a brief introduction to integration.

250102 Calculus II Techniques of integrations, Conic sections, Polar coordinates, Intermediate forms, Improper integrals, Vectors, Sequences, and Infinite series. Prerequisite: 210101

250151 Discrete Mathematics Sets, relations, and functions. Mathematical induction. Recursion. Propositional logic. Counting techniques. Elements of combinatorics. Introduction to graphs and trees.

200 level

210231 Introduction to Probability and Statistics This is an introductory course in statistics. The course is planned so that students learn the basic concepts needed in probability theory and statistics. It familiarizes students with statistical terms such as population, sample, sample size, random variable, mean, variance, and much more. The course covers materials such as collecting data, graphical methods, descriptive statistics, regression and correlation, probability basics, confidence intervals and hypothesis testing.

210235 Biostatistics This course provides a practical introduction to statistical methods used in a variety of disciplines, such as health sciences, pharmacology, and nursing. All concepts introduced in the course are illustrated with examples that demonstrate principles. Materials covered are Picturing Distributions With Graphs, Numerical Summaries, The Normal Distribution, Standard Normal Distribution, Correlation and Regression, The Sampling Distribution of The Mean, Confidence Intervals, and Test of Hypotheses for the Mean.

250201 Intermediate Analysis Multidimensional analytic geometry, functions of several variables, vector-valued functions, partial derivatives, gradiant, maxima-minima problems and applications, double and triple integrals; potential fields; flux; Green's divergence and Stokes' theorems. Prerequisite: 250102

250203 Ordinary Differential Equations First and second-order equations; numerical methods; special functions; Laplace transform solutions; higher order equations. Prerequisite: 250201

250232 Probability Theory This course provides a practical introduction to probability theory. The materials covered in this course represent the corner stone of much of what will be needed in statistical inference in the future. All concepts introduced in the course are illustrated with examples that demonstrate principles. The course covers materials such as Counting Techniques, Probability Axioms, Discrete and Continuous Random Variables, The Moment Generating Function, The Bivariate Distribution, Joint, Marginal, and Conditional Distributions, Independence, Correlation and Covriance.

250241 Linear Algebra I Vector spaces, matrices, determinants, Linear transformations, Gauss Jordan elimination, eigenvalues and eigenvectors, theory and applications. Prerequisite: 210101

250251 Set Theory Logic and proofs, Sets, set operations, cardinal numbers, finite sets, orders, axiomatic set theory, well-ordering, cardinals and ordinals, the axiom of choice. Prerequisite: 250102

250261 Modern Euclidean Geometry Axioms of Euclidean geometries, isomorphisms and models, Finite geometry, Neutral geometry, equivalence of the parallel postulate, hyperbolic geometry. Projective geometry. Prerequisite: 250251

300 level

210331 Design of Experiments (Elective Course) This course is designed to introduce the student to the basic ideas of experimental design and accompanying analysis. It also enriches student's knowledge and understanding of the statistical methods as it pertains to the design and analysis of experiments. Emphasis will be on conceptual understanding and application to practical problems. Students completing the course are expected to be knowledgeable in the basic experimental designs. Materials covered in the course include Introduction to Statistics and Data Analysis, Inferential Data Analysis for Simple Experiments, One Factor Designs, One Factor Blocking Designs, Latin Square Designs, Two- and General Factor Factorial Experimental Designs, 2K Factorial Designs. Prerequisite: 210232

210332 Applied Probability (Elective Course) Spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems. Prerequisite: 210231

250305 Partial Differential Equations Partial differential equations, orthogonal functions, Sturm-Liouville boundary value problems, Green's functions, variational methods, and other topics. Prerequisite: 250203

250311 Real Analysis I Analytical study on real variable, basic topology, metric spaces, sequence and series, power series, limit, derivatives, integrations, the Riemann Stieltjes Integral. Prerequisite: 250151

250312 Complex Analysis Functions of one complex variable, limits, derivatives, analytic functions, integrations, contour integrals, Cauchy's Theorem, Fundamental Theorem of Algebra, Power Series, Convergence, Residues and Poles. Prerequisite: 250311

250313 Number Theory Studies of the integers: divisibility, prime numbers, the Fundamental Theorem of Arithmetic, the theory of congruences and applications, primitive roots and applications, quadratic reciprocity, and selected cryptographical applications. Prerequisite: 250102

250321 History of Mathematics (Elective course) An overview of different subjects of mathematics from the historical point of view. Topics may vary. Origin of numbers, the ancient Orient, works of Socrates, Euclid, Archimedes, Islamic period, western Europe, transition to modern mathematics, discovery of Calculus, development of algebra, geometry, probability, selected topics.

250332 Mathematical Statistics This is an introductory course in mathematical statistics. Topics will include Functions of Random Variables, Sums of Random Variables, Order Statistics, Point Estimators and Their Properties, Confidence Intervals and Test of Hypotheses. Prerequisite: 250232

250341 Linear Algebra II An advanced study of linear algebra: vector spaces, subspace, linear independence, bases, linear transformation, determinants, eigenvalues, diagonalization, inner product space, linear operator, selected topics on canonical form. Prerequisite: 250241

250342 Abstract Algebra I Studies in the theory of groups, cyclic groups, isomorphism theorems, the fundamental theorem of finite abelian groups, symmetry groups, Sylow theorems or other selected topics. Prerequisite: 250251

250351 Graph Theory (Elective Course) Studies in graph theory, Eulerian circuits, trees, shortest path problem, matchings, graph coloring, planar graph, Hamiltonian cycles, matrical representations, digraphs, various applications and algorithms. Prerequisite: 250251

250371 Numerical Analysis Techniques of numerical solutions to various mathematical problems, solutions of equations, Newton's method, zeros of polynomials, interpolations, numerical differentiations and integrations, numerical differential equations, initial value problems, systems of linear equations, matrix inverse, determinants, and eigenvalues. Prerequisite: 250241, 250203

250372 Computer Aided Mathematics Symbolic computational packages and scientific visualization through examples from calculus and geometry. Prerequisite: department agreement

250381 Problem Solving Concepts in problem solving; practice in solving a wide variety of mathematical and logical problems; techniques for attacking problems; building mathematical models. Prerequisite: 60 credit hours

250383 Psychology of Learning and Learning Theories (Elective Course)

400 level

250411 Real Analysis II Continuation of 250311, series of functions, uniform convergence, the Stone Weierstrass theorem, the exponential function, algorithmic function, Fourier series, differential forms, vector analysis, Lesbegue measure. Prerequisite: 250311

250412 Functional Analysis (Elective Course) Compact operators and Fredholm theory, Banach algebras, harmonic analysis, differential equations, nonlinear functional analysis, and Riemann surfaces. Prerequisite: 250311

250442 Abstract Algebra II Studies in rings and fields, ideals, integral domains, rings of polynomials, vector spaces, extension fields, Galois theory, finite fields and selected applications. Prerequisite: 250342

250451 Philosophy of Mathematics (Elective Course) Selected topics from philosophy of mathematics and historical point of view.

250461 Topology Point-set metric spaces, topological spaces, product spaces, identification spaces, compactness and connectedness, countabiliy, separation axioms, complete metric spaces. Prerequisite: 250311

250462 Algebraic Topology (Elective Course) Fundamental groups and covering spaces, separation theorems in the plane, the Seifert-van Kampen theorem, homology of surfaces, and related topics. Prerequisite: 250461, 250342

250471 Mathematical Modeling Construction, development, and study of mathematical models for real situations; basic examples, model construction, Markov chain models, models for linear optimization, selected case studies. Prerequisite: 250102 and 250241

280472 Computational Number Theory Basics of number theory: divisibility, primes, congruences; Overview of Public-Key Cryptography, RSA algorithm, Factoring algorithms, Pseudoprimes, Primality testing, topics in prime number search and related algorithms. Prerequisite: 710102, 250313

250473 Advanced Applied Mathematics (Elective Course) Covers integral theorems of vector analysis, complex variables, series solutions to differential equations, Laplace and Fourier transforms, and use of mathematical software languages such as Maple and Mathematica. Prerequisite: 250311

250474 Control Theory (Elective Course) topics in optimization problems; linear, nonlinear, and integer programming. Prerequisite: 250241

250476 Game Theory Basic theorems, concepts, and methods in the mathematical study of games of strategy; determination of optimal play when possible. Prerequisite: 250241

250481 Instructional Strategies for Teaching Mathematics The student will study and participate in instructional activities and strategies for mathematics that depart from the lecture style; e.g., cooperative learning or open-ended problem exploration. Students will design and conduct a mathematics lesson using such a strategy. Prerequisite: must have completed 90 credit hours.

280482 Pedagogy of Mathematics Prerequisite: must have completed 90 credit hours

280491 Seminar Students' seminar series. Prerequisite: Department's agreement

280492 Special Topics Individual guided study. Prerequisite: Department's agreement