Undergraduate Catalog 2006-07 - DRC Home - Walsh University
Undergraduate Catalog 2006-07 - DRC Home - Walsh University Undergraduate Catalog 2006-07 - DRC Home - Walsh University
on the many practical uses of mathematics in our society. This is a course in mathematical literacy, not manipulative techniques. Topics are selected from the environment, politics, polling, social ethics, choice and decision making, technology, management, statistics, size, shape and art. Prerequisite: one year of high school algebra. Recommended for non-science majors. Offered every semester. MATH 120 Ethnomathematics 3 sem. hrs. Indigenous peoples provide examples of the concept of number, related symbols, graph theory (eg. sand paintings), kin relations, games of strategy and chance, logic of puzzles, organization of time and space, spatial configurations. Cultures selected from South America, Africa, Russia, Australia, Native American, Inuit, Maori. Increases understanding of mathematics and of other peoples. Prerequisite: High school algebra and geometry. Recommended for non-science majors. Credit in Diversity Cluster. Offered every fall semester. MATH 130 Mathematics and 3 sem. hrs. the Environment Shapes and patterns in nature are examined through various media thereby heightening awareness and appreciation of our environment. A special area of environmental concern, such as air or water quality, is explored in depth through examining data using mathematical modeling and appropriate technology. Prerequisite: High school algebra and geometry. Credit in the Environment Cluster. Offered even-numbered falls. MATH 155-156 Elementary 3 sem. hrs. ea. Functions I and II (Formerly MATH 105-106) Algebraic foundations, functions and graphs, polynomial functions, rational functions, exponential functions, logarithms and logarithmic functions, complex numbers, basic trigonometry, trigonometric identities, trigonometric equations, trigonometric functions, inverse trigonometric functions. Prerequisite FOR 155: two years of high school algebra and one year of high school geometry; Prerequisite for 156: MATH 155. Offered every semester. MATH 160 Euclidean Geometry 3 sem. hrs. Axiomatic and transformational geometry, originated by Euclid, modified by Descartes and others. Points, lines, angles, parallels, planes, space, triangles, polygons, circles, measurement, congruency, similarity, area, volume, coordinates, isometries, constructions. Emphasis on deductive reasoning. Use of ancient tools and modern technology. Foundation for teaching of geometry and further study of modern geometries. Prerequisite: high school algebra and geometry. Offered odd-numbered springs. MATH 207 Calculus I 5 sem. hrs. Limits, continuity, derivitaves, anti-derivatives, integration and the fundemental theorem of calculus. Prerequisite: MATH 156 or placemnt. Offered every semester. MATH 208 Calculus II 4 sem. hrs. Transcendental functions, methods of integration, improper integrals, sequences and series, Taylor series, polar coordinates, parametric equations. Prerequisite: MATH 207 with a grade of C or better. Offered every semester. MATH 221 Statistics 3 sem. hrs. Elementary theory of probability and statistics, frequency distributions, binomial distributions, normal distributions, means, variances, standard deviations, sampling, confidence limits, testing of hypotheses, applications drawn from real world situations. Does not count toward the 33 hours required for a major in Mathematics. Prerequisite: MATH 104 or equivalent. Offered every semester. MATH 220 Finite Mathematics 3 sem. hrs. Systems of linear equations; Matrices including basic operations and inverse of a square matrix; Systems of linear inequalities; Linear programming including the simplex method; Logic and Sets; Basic Counting Principles; Permutations and Combinations; Elementary probability theory including equiprobable models, conditional probability and Bayes' theorem; Markov Chains including regular Markov Chains and absorbing Markov Chains. Prerequisite: MATH 104 or equivalent. MATH 230-231 Discrete Patterns I & II 3 sem. hrs. ea. (See Computer Science 230-231) Algorithms and Combinatorics. Logic, circuits, Karnaugh maps. Proofs, including quantified statements and mathematical induction. Relations, graphs, trees. Languages and finite-state machines. Prerequisite for 230: One year college algebra or MATH 155 or equivalent with permission; Prerequisite for 231: MATH 230. 230 offered every spring; 231 offered every fall. MATH 255 Complex Variables I 3 sem. hrs. Introduction to complex numbers and their geometry, functions of one complex variable and their differentiation and the fundamental theorem of algebra. Prerequisite: MATH 205. MATH 307 Calculus III 4 sem. hrs. Vectors, analytic gometry of three-dimensional space, partial derivitaves, multiple integrals, theorems of Green and Stokes. Prerequisite MATH 208 with a grade of C or better. Offered every semester. MATH 313-314 Linear Algebra I & II 3 sem. hrs. ea. Concepts, algorithms, proofs and applications over these topics: systems of linear equations, matrices, determinants, finite-dimensional vector spaces, eigenvalues, orthogonality, quadratic forms. Related topics may be included such as complex numbers, base transformation, linear programming. Prerequisite for MATH 313: MATH 207 and MATH 230 or permission of the instructor; Prerequisite for MATH 314: grade of C or better in MATH 313. MATH 313 is required for the Mathematics major and strongly recommended for the Computer Science major. MATH 313 offered every fall; MATH 314 offered odd-numbered springs. MATH 321-322 Probability and 3 sem. hrs. ea. Statistical Inference I & II Introduction to probability theory, random sampling, classical and nonparametric statistics. Prerequisite for 321: MATH 207; prerequisite for 322: MATH 321. 321 offered even-numbered falls; 322 offered odd-numbered springs. MATH 299/399 Special Topics 3 sem. hrs. To fill special student needs or take advantage of a visiting professor or serve as an experimental offering of a contemplated regular course. May be repeated as new topics are presented. With permission of department chair. MATH 402 Introduction to Modern 3 sem. hrs. Geometry Study of axiomatic and transformational geometries selected from finite geometry, Euclidean geometry, projective geometry, non- UNDERGRADUATE CATALOG 135
Euclidean geometries, fractal geometry, and topology. Prerequisite: MATH 313. Offered odd-numbered falls. MATH 405 Introduction to Modern 3 sem. hrs. Analysis I Logic and proofs applied to continuous domains. Sets, functions and coordinality. Natural numbers and induction; ordered fields and the completeness axiom and compact sets. Sequences: convergence, limit theorems, monotone and cauchy sequences, subsequences. Prerequisites: MATH 230 and MATH 307. Offered odd-numbered falls. MATH 406 Introduction to Modern 3 sem. hrs. Analysis II Limits and continuity, uniform continuity; differentiation, l'Hôpital's Rule, Taylor's theorem; the Riemann integral and the Fundamental Theorem of Calculus; infinite series and convergence tests; sequences and series of functions. Prerequisite: MATH 405. Offered times depend on demand. MATH 410 Elementary Differential 3 sem. hrs. Equations Equations of first and second orders, linear equations with constant coefficients, solutions in series, numerical approximations. Prerequisite: MATH 313, 307. Offered even-numbered springs. MATH 421 Introduction to Modern 3 sem. hrs. Algebra I Theoretical, axiomatic approach to algebraic structures. Mappings, equivalence relations, groups, homomorphisms, rings, ideals. Prerequisite: MATH 313 and 307. Offered even-numbered falls. MATH 422 Introduction to Modern 3 sem. hrs. Algebra II Continuation of MATH 421. Groups, rings, ideals, fields, integral domains, polynomials, vector spaces. Prerequisite: MATH 421. Offered times depend on demand. MATH 490 Independent Study/Research 3 sem. hrs. With permission of the Division Chair and Vice President for Academic Affairs. By arrangement. MIDDLE CHILDHOOD EDUCATION (MCE) MCE 222 Middle Childhood: 3 sem. hrs. Philosophy, Org., & Instruction Characteristics of and rationale for middle level schools are examined. Concepts such as interdisciplinary teams, flexible organizational structure, teacher-based guidance programs, classroom management, family and community relations, and exploratory, integrative curricula are included. Field hours required. Prerequisites: EDUC 107 and sophomore standing. Offered fall and spring semesters. MCE 223 Young Adolescent 3 sem. hrs. Psychology Learning theories and instructional models relating to young adolescents are examined from a practical classroom-based perspective. Focus is on interpreting and integrating educational concepts to address various learning situations in a middle level classroom. Physical, social, emotional, intellectual, and moral characteristics of 136 2006-2007 WALSH UNIVERSITY early adolescence are included. Developmentally and culturally responsive instruction is emphasized. Prerequisites: EDUC 107 and sophomore standing. Required for 300/400-level classes. Offered every semester. Admission to the Teacher Preparation Program required prior to enrollment in 300-/400-level education courses. MCE 420 Middle Childhood: Teaching, 3 sem. hrs. Learning, and Assessment Emphasis on the design, implementation and assessment of teaching and learning approaches appropriate for young adolescents. Focus on various teaching and learning strategies and assessment alternatives that promote the learning of young adolescents. Field experience included. Offered fall and spring semesters. MCE 421 Middle Childhood: 9 sem. hrs. Student Teaching Theory and practice are implemented in actual teaching in a middle level school environment. Developing skills in ten Ohio performance-based licensure areas as appropriate for middle childhood licensure is emphasized. Conferences held with university supervisor and cooperating teacher. 14 week experience. Prerequisite: all coursework leading to MCE licensure. Taken with MCE 422. Offered fall and spring semesters. MCE 422 Middle Childhood: Student 3 sem. hrs. Teaching Seminar This capstone seminar accompanies the clinical practice and serves as the Heritage III requirement for Education students. The seminar provides for the integration of experience in the liberal arts tradition which enables students to respond to the contemporary challenges of the 21st century posed by the teaching profession today. Prerequisites: all coursework leading to Middle Childhood licensure. Course to be taken concurrently with student teaching (MCE 421). Offered fall and spring semesters MCE 423 Middle Childhood 1.5 sem. hrs. Professionalism in Practice: Language Arts Pre-Student Teaching Writing process models, whole language and multimedia approaches for teaching composition and literature for those seeking licensure at the middle level. Various instructional strategies, assessment alternatives, classroom management, and provisions for dealing with individual differences among students when using these approaches is emphasized. Attention to NCTE standards and Ohio Academic Content Standards. Field experience included. All coursework and the appropriate Praxis II content test(s) must be successfully completed in order for student teaching to occur the following semester. Course to be taken semester prior to student teaching. Offered fall and spring semesters. MCE 424 Middle Childhood 1.5 sem. hrs. Professionalism in Practice: Mathematics Pre-Student Teaching Course designed for those seeking licensure at the middle level. Focus on methods of instruction appropriate to and issues associated with teaching mathematics. Incudes an examination of appropriate uses of technology and of how NCTM standards and Ohio Academic Content Standards have impacted the curriculum, day-to-day activities, and assessment approaches. Field experience included. All coursework and the appropriate Praxis II content test(s) must be suc-
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Euclidean geometries, fractal geometry, and topology. Prerequisite:<br />
MATH 313. Offered odd-numbered falls.<br />
MATH 405 Introduction to Modern 3 sem. hrs.<br />
Analysis I<br />
Logic and proofs applied to continuous domains. Sets, functions<br />
and coordinality. Natural numbers and induction; ordered fields<br />
and the completeness axiom and compact sets. Sequences: convergence,<br />
limit theorems, monotone and cauchy sequences, subsequences.<br />
Prerequisites: MATH 230 and MATH 3<strong>07</strong>. Offered<br />
odd-numbered falls.<br />
MATH 406 Introduction to Modern 3 sem. hrs.<br />
Analysis II<br />
Limits and continuity, uniform continuity; differentiation, l'Hôpital's<br />
Rule, Taylor's theorem; the Riemann integral and the Fundamental<br />
Theorem of Calculus; infinite series and convergence tests;<br />
sequences and series of functions. Prerequisite: MATH 405. Offered<br />
times depend on demand.<br />
MATH 410 Elementary Differential 3 sem. hrs.<br />
Equations<br />
Equations of first and second orders, linear equations with constant<br />
coefficients, solutions in series, numerical approximations.<br />
Prerequisite: MATH 313, 3<strong>07</strong>. Offered even-numbered springs.<br />
MATH 421 Introduction to Modern 3 sem. hrs.<br />
Algebra I<br />
Theoretical, axiomatic approach to algebraic structures. Mappings,<br />
equivalence relations, groups, homomorphisms, rings, ideals.<br />
Prerequisite: MATH 313 and 3<strong>07</strong>. Offered even-numbered falls.<br />
MATH 422 Introduction to Modern 3 sem. hrs.<br />
Algebra II<br />
Continuation of MATH 421. Groups, rings, ideals, fields, integral<br />
domains, polynomials, vector spaces. Prerequisite: MATH 421.<br />
Offered times depend on demand.<br />
MATH 490 Independent Study/Research 3 sem. hrs.<br />
With permission of the Division Chair and Vice President for<br />
Academic Affairs. By arrangement.<br />
MIDDLE CHILDHOOD<br />
EDUCATION (MCE)<br />
MCE 222 Middle Childhood: 3 sem. hrs.<br />
Philosophy, Org., & Instruction<br />
Characteristics of and rationale for middle level schools are examined.<br />
Concepts such as interdisciplinary teams, flexible organizational<br />
structure, teacher-based guidance programs, classroom management,<br />
family and community relations, and exploratory, integrative<br />
curricula are included. Field hours required. Prerequisites: EDUC<br />
1<strong>07</strong> and sophomore standing. Offered fall and spring semesters.<br />
MCE 223 Young Adolescent 3 sem. hrs.<br />
Psychology<br />
Learning theories and instructional models relating to young adolescents<br />
are examined from a practical classroom-based perspective.<br />
Focus is on interpreting and integrating educational concepts to<br />
address various learning situations in a middle level classroom.<br />
Physical, social, emotional, intellectual, and moral characteristics of<br />
136 <strong>2006</strong>-20<strong>07</strong> WALSH UNIVERSITY<br />
early adolescence are included. Developmentally and culturally<br />
responsive instruction is emphasized. Prerequisites: EDUC 1<strong>07</strong> and<br />
sophomore standing. Required for 300/400-level classes. Offered<br />
every semester.<br />
Admission to the Teacher Preparation Program required prior<br />
to enrollment in 300-/400-level education courses.<br />
MCE 420 Middle Childhood: Teaching, 3 sem. hrs.<br />
Learning, and Assessment<br />
Emphasis on the design, implementation and assessment of teaching<br />
and learning approaches appropriate for young adolescents. Focus on<br />
various teaching and learning strategies and assessment alternatives<br />
that promote the learning of young adolescents. Field experience<br />
included. Offered fall and spring semesters.<br />
MCE 421 Middle Childhood: 9 sem. hrs.<br />
Student Teaching<br />
Theory and practice are implemented in actual teaching in a middle<br />
level school environment. Developing skills in ten Ohio performance-based<br />
licensure areas as appropriate for middle childhood licensure<br />
is emphasized. Conferences held with university supervisor and<br />
cooperating teacher. 14 week experience. Prerequisite: all coursework<br />
leading to MCE licensure. Taken with MCE 422. Offered fall<br />
and spring semesters.<br />
MCE 422 Middle Childhood: Student 3 sem. hrs.<br />
Teaching Seminar<br />
This capstone seminar accompanies the clinical practice and serves<br />
as the Heritage III requirement for Education students. The seminar<br />
provides for the integration of experience in the liberal arts tradition<br />
which enables students to respond to the contemporary challenges of<br />
the 21st century posed by the teaching profession today.<br />
Prerequisites: all coursework leading to Middle Childhood licensure.<br />
Course to be taken concurrently with student teaching (MCE<br />
421). Offered fall and spring semesters<br />
MCE 423 Middle Childhood 1.5 sem. hrs.<br />
Professionalism in Practice: Language<br />
Arts Pre-Student Teaching<br />
Writing process models, whole language and multimedia approaches<br />
for teaching composition and literature for those seeking licensure<br />
at the middle level. Various instructional strategies, assessment alternatives,<br />
classroom management, and provisions for dealing with<br />
individual differences among students when using these approaches<br />
is emphasized. Attention to NCTE standards and Ohio Academic<br />
Content Standards. Field experience included. All coursework and<br />
the appropriate Praxis II content test(s) must be successfully completed<br />
in order for student teaching to occur the following semester.<br />
Course to be taken semester prior to student teaching. Offered fall<br />
and spring semesters.<br />
MCE 424 Middle Childhood 1.5 sem. hrs.<br />
Professionalism in Practice:<br />
Mathematics Pre-Student Teaching<br />
Course designed for those seeking licensure at the middle level.<br />
Focus on methods of instruction appropriate to and issues associated<br />
with teaching mathematics. Incudes an examination of appropriate<br />
uses of technology and of how NCTM standards and Ohio Academic<br />
Content Standards have impacted the curriculum, day-to-day activities,<br />
and assessment approaches. Field experience included. All<br />
coursework and the appropriate Praxis II content test(s) must be suc-