MATH 103. The Nature of Mathematics. 3 credits.
This course is specifically designed for the liberal studies/general education program as an option to the more traditionalofferings in mathematics which concentrate in prescribed areas. Flexibility in the choice of content modulesprovides students a variety of opportunities to experience careful articulationof problems, the powers of abstraction, the use of logic and deduction, and thedifference between determinism and probability.
Through the rigorous analysis of carefully selectedmodules,students develop investigative and communicative skills in mathematics. They broaden their intellectual foundationsand critical facilities by seeing examples of what mathematicians seek to doand how they do it. Most importantly,the course seeks to shape attitudes toward mathematics as a worthwhile humanendeavor whose benefits can be used andappreciated.
Mathematics is the language of our increasinglytechnological age. To achieve fullrealization of potential, all persons need facility in and understanding ofthis subject. Math 103 helps theliberal studies/general education student meet this need.
Sample Syllabi:
1) (a) Arithmetic,geometry, and problem solving in ancient Egypt and ancientIraq.
(b) The mathematics of Thales and thePythagorean school.
(c) The mathematics of Greece in the 4th and5th centuries BC.
(d) The mathematics of the Hellenistic worldwith special emphasis on topicsthat are still in vogue (Pythagorean Theorem,incommensurables, conic sections,etc.).
2) (a) Permutationsand combinations, probability, conditional probabilityand independence withapplications to gambling and the fifteen puzzle.
(b) Cryptography.
(c) Modular arithmetic.
(c) Topics from History of Mathematics.
3) (a) Axiomaticsystems and the field axioms.
(b) First order logic and proof.
(c) First degree equations and systems offirst degree equations..
(d) Quadratic equations.
4) (a) Additionand multiplication of ordered pairs of numbers.
(b) The field "axioms" as theoremsin this system.
(c) First degree equations.
(d) Quadratic equations.
Math 103 is a LEVEL I course and satisfies the liberal studies requirement in mathematics. Thespecific objectives for the course are: 1. (a)-(e)
MATH 107-108. Fundamentals of Mathematics. 3 credits.
Problem solving and critical thinking are fundamental to allactivities in the discipline of mathematics and are the main themes of thesetwo courses. Since problems areselected from many other fields, these courses make a connection between mathematics as a whole and other areas. The sequence Math 107-108 is designed to satisfy liberal studiesrequirements with a special emphasis on students who wish to become teachers inelementary and middle school.
The subject matter of the courses includes a consideration of several of civilization's greatest achievements, including the real number system, the Hindu-Arabic numeration system, and Euclidean geometry. These subjects are fundamental to humanknowledge. The study of these topicsincludes some consideration of their historical origins in ancientcultures. Thus, the courses explore thepurpose of mathematics, its limits, and its successes and failures.
The courses include topics which are very practicalas wellas useful in intellectual development. These include logical reasoning, elementary probability theory, descriptive statistics, and an introduction to computers. These topics provide students with increasedunderstanding of mathematics as a worthwhile human endeavor with immediate anduseful benefits.
Syllabi:
1) Math 107 (a) Critical thinking.
(b) Problem solving.
(c) Logic.
(d) Sets.
(e) System of whole numbers.
(f) Numeration systems.
(g) Introduction to computing.
(h) Number theory.
(i) System of integers.
2) Math 108 (a) Introduction to geometry.
(b) Transformations in geometry.
(c) Additional topics in geometry.
(d) Introduction to probability.
(e) Statistics.
Math 107 and Math 108 are LEVEL I courses and satisfy theliberal studies requirement in mathematics. The specific objectives for the courses are: 1. (a)-(d)
The subject matter of these courses is particularlyusefulin the elementary and middle school classroom. Each serves as an elective for any student wishing to become anelementary or middle school teacher. The sequence satisfies the B.S. requirement in mathematics.
MATH 135. Elementary Functions. 3 credits.
Algebraic, exponential, logarithmic and trigonometric functions are studied as the building blocks of calculus and analysis. Math 135 is designed for freshmen who needto improve their competency in theseareas and who plan to take MATH 235 (Analytic Geometry and Calculus, 4 credits). The needs of these students require that thecourse be highly focused on skills whose applications, values and connectionsto other disciplines largely will not be realized until later. The liberal studies components which arepresent in this course are not fully realized until the student completes MATH235.
Syllabus:
(a) Basic algebra.
(b) Functionsand their graphs.
(c) Exponentialand logarithmic functions.
(d) Trigonometricfunctions.
(e) Trigonometricidentities and equations.
(f) Applicationsof trigonometry.
(g) The complexnumber system.
Math 135 will satisfy 3 hours of the B.S. requirement inmathematics. This course does notsatisfy the liberal studies requirement in mathematics. The specific objectives of this course areto prepare students to take a follow up course that requires specific basicskills to succeed.
MATH 155. Functionsand Probability. 3 credits.
(MATH 156. Functions and Probability. 3 credits. 1 hr. lab.)
Polynomial, rational and logarithmic functions andapplications, systems of equations and inequalities, sequences, counting andprobability are studied as the building blocks for calculus and statisticsapplications to biological, social and management sciences.
MATH 155(156) is designed for freshmen who need to improve their competency in these areas and who plan to take MATH 205. The needs of these students require that thecourse be highly focused on skills whose applications, values and connectionsto other disciplines largely will not be realized until later. The liberalstudies components which are present in this course are not fully realizeduntil the student completes MATH 205 (Introduction to Calculus, 3 credits).
Syllabus:
(a) Review of numbers and their properties,exponents and polynomials,equations and inequalities, coordinates and curves.
(b) Functions and their graphs.
(c) Exponential and logarithmic functions.
(d) Systems of equations and systems ofinequalities.
(e) Sequences and counting problems.
(f) Probability and expectation.
Math 155(156) will satisfy 3 hours of the B.S. requirement in mathematics. This coursedoes notsatisfy the liberal studies requirement in mathematics. The specific objectives of this course areto prepare students to take a follow up course that requires specific basicskills to succeed. Math 156 differsfrom Math 155 in that the course meets four hours per week and so the pace ofthe course is slower.
MATH 205-206. Introductory Calculus. 3 credits.
Math 205-206 is a two semester sequence of introductory calculus designed for non-mathematics majors. Calculus is a fundamental area of human knowledge that has greatly influenced our understanding of the world around us. Students have an opportunity in MATH 205-206 to experienceanintroduction to the concepts of calculus as they apply to disciplines suchasthe behavioral and life sciences and business. The topics are presented in an informal manner, so the studentdevelopsan intuitive grasp of the subject. Theopportunities offered in this course of working throughoptimization,exponential growth and decay, rates of change, and other problems,allow thestudent to develop rigorous analytical skills and to see in a directway howmathematicians use mathematics to learn about the real world. The student will appreciate that mathematicsis a highly developed language that permits one to communicate effectively in,and better understand, our modern high-technology age.
Course Outline:
1. Precalculus Review
2. Limits of Functions, Continuity
3. The Derivative
4. Rules of Differentiation (Product/Quotient Rules, The ChainRule)
5. Applications of the Derivative: Optimization and Curve Sketching
6. Exponential and Logarithmic Functions and their Derivatives; Applications
7. Antiderivatives (the Indefinite Integral); the Method ofSubstitution
8. The Definite Integral; Area
9. The Fundamental Theorem of Calculus; Evaluating Definite Integrals; Applications
Math 205 is a LEVEL I course and satisfies the liberal studies requirement in mathematics.. The specific objectives for the course are: 1. (a), (b), 2. (a), (c)
The applications in this course are specifically chosen forbehavioral and life sciences and business students. This course is a valuable elective for majors in thesedisciplines.
2) Math 206 (a) Areasbetween curves.
(b) Volumes of solids of revolution.
(c) Average value of a function.
(d) Partial derivatives.
(e) Extrema of functions of several variables.
(f) Lagrange multipliers and constrained optimization.
(g) Total differentials and their applications.
(h) Method of least squares.
(i) Double integrals.
(j) Trigonometric functions, their derivatives and applications.
(k) Integration by substitution.
(l) Integration by parts.
(m) Approximation of definite integrals.
(n) Improper integrals.
(o) Differential equations.
Math 206 is a LEVEL I course and satisfies the liberal studies requirement in mathematics.. Thespecific objectives for the course are: 1. (a), (b) 2.(b), (c) 3. (f)
The applications in this course are specifically chosen forbehavioral and life sciences and business students. This course is a valuable elective for majors in these disciplines. The sequence satisfies the BS requirement inmathematics.
MATH 220. Elementary Statistics. 3 credits.
This course is designed to expose non-mathematics majors tothe basic concepts and methods of statistics most commonly used in a variety ofdisciplines. The topics covered includedescriptive statistics, frequency distributions, sampling, estimation andtesting of hypotheses, regression, correlation, and an introduction to statistical analysis using computers.
Employing real life examples from various areas, the students are led to more fully appreciate the intrinsic uncertain aspects ofthe real world--physical, biological, social-economic-political, andbehavioral-psychological. The studentsare taught to read and understand the information given, logically put it touse in making decisions, and clearly express their conclusions. In doing so, the underlying assumptions ofthe statistical methods and the intrinsic limitations of the conclusions (dueto the assumptions imposed and the probabilistic nature) are alwaysemphasized. In particular, the studentsare taught to distinguish sound statistical procedures and statements fromfallacious ones and to guard against the misuse and abuse of statistics. In this way, the students learn the basicstatistical methods used in various disciplines to gain new knowledge and solveproblems about the real world, and, at the same time, learn to appreciate thelimitations of such methods and the knowledge and solutions thus obtained. In addition, the computer component of thiscourse introduces the students to the use of this indispensable tool foranalyzing data andsolving problems in the modern world.
Statistics is a basic tool for obtaining new knowledge: it is a guide to the unknown. Statistics is widely used not only in thesciences but alsoin education, business, industry, government, the humanities,and societyin general. Modern manlivesin a world of constant flux and saturation of information, which can beorganizedonly through the use of statistics. Thus, statistics is a subject every educated man and woman in themodernworld can use. With itsemphasis on thebasic concepts and methods commonly used in various disciplines rather thanspecific to any particular discipline, MATH 220 is a very suitable course forthe Liberal Studies Program.
Topics in Math 220
a) Mean, median, mode, percentiles, range,variance, standard deviation, Interquartile range,
b) Stemand leaf, (modified) box plot
c) Frequencyand relative frequency Histograms
a) Categoricaldata tables (counts, percents, probabilities)
b) Scatterdiagram
c) CorrelationCoefficient
d) Estimationof the slope and intercept for a simple linear regression model
a) Anintroduction – short
b) RandomVariables – mean and variance
c) DetermineBinomial probabilities
a) Modelfor a continuous random variable
b) Generalfeatures and properties
c) StandardNormal – use of table
d) Probabilitycalculations (standardizing)
a) Distributionof the sample mean
b) CentralLimit Theorem
a) Pointestimate
b) Intervalestimate
c) Hypothesistesting - P value method
a) Testfor Homogeneous populations
b) Testfor Independence
Math 220 is a LEVEL I course and is an elective in the statistics minor for non-mathematics majors. The specific objectives for the course are: 1. (a), (b), S2. (a)- (h).
This course satisfies the liberal studies requirement inmathematics and serves as an elective for any student not specializinginmathematics. The subject matterof thiscourse has wide application and so this course is an elective forseveralmajors across campus.
MATH 235-236-237. Calculus and Analytic Geometry. 4creditseach semester.
This is a three semester sequence of courses that integrates the subject matter of analytic geometry, differential and integral calculus andinfinite series. The concept of a limitis formalized and studied as the basis for the definitions of such concepts ascontinuity, differentiability, integrability and convergence. The applications of these definitions leadto the development of a collection of theorems that constitute a most powerfularsenal for successful problem solving. The sequence serves as a model for the development of mathematics fromtheory to application and sets a tone for the future study of mathematics.
Calculus is a language used to describe and understand thenatural world. In an increasingly technological age, it is essential that educated persons have someunderstanding of quantitative analysis. The models developed in these courses are important not only in the"obvious"application to the physical sciences, but they are alsoused with growingregularity in the social sciences
Syllabi:
1) Math 235
Pre-calculus
Limitsand Continuity
Differentiation
Optimizationand Curve Sketching
TheDefinite Integral
TheFundamental Theorems of Calculus
Applicationsof the Definite Integral
Math 235 is a LEVEL I course and is required in themathematics major. The specificobjectives for the course are: 1. (a), (b), (c), 2. (a), (b), 3. (c),(f), 4. (a)-(d)
This course is a required course for any student wishing tominor in mathematics. Thesubjectmatter for this course has wide applications and so this course isa valuableelective for non-specialists.
2) Math 236 (a) Inverse functions.
(b) Logarithmic and exponential functions.
(c) Inverse trigonometric functions.
(d) Techniques of integration.
(e) Polar coordinates.
(f) Indeterminate forms (L'Hopital's rule).
(g) Improper integrals.
(h). Convergence and divergence of sequenceand series
(i). Comparison test, ratio test, limit ratiotest.
(j). Alternating series, absolute convergenceand conditional convergence.
(k). The Taylor remainder theorem and Taylorseries.
(l). Power series and Maclaurin's series.
(m). Radiusof convergence.
(n). Algebraic properties of power series.
(o). Differentiation and integration of powerseries.
Math 236 is a LEVEL I course and is required in themathematics major. The specificobjectives for the course are: 1. (a), (b), (c), 2. (b), (c), 3. (d), (g),(l)
This course is a required course for any student wishing tominor in mathematics. Thesubjectmatter for this course has wide applications and so this course isa valuableelective for non-specialists.
3) Math 237
(a) Vectors
1. Vectorsin R2.
2. Vector-valuedfunctions and parametric equations.
3. Vectors in R3.
(b) Curves and surfaces
1. Planesand lines in R3.
2. Cylinders and surfaces of revolution.
3. Quadric surfaces.
4. Space curves.
(c) Multivariate Calculus.
1. Functions, limits and continuity.
2. Partial derivatives and the totaldifferential.
3. The chain rule.
4. The gradient and directionalderivatives.
5. Tangent plane and normal line.
6. Extrema and constrained extrema.
7. Implicit functions.
(d) Integration Theory.
1. Double integrals and iteratedintegrals.
2. Applications of double integrals.
3. Triple integrals.
4. Integration in polar, cylindrical andspherical coordinates.
5. Line and surface integrals.
Math 237 is a LEVEL I course and is required in themathematics major. The specificobjectives for the course are: 1. (a), (b), (c), 3. (d), (e), (f), (l) 4.(e)
This course is a required course for any student wishing tominor in mathematics. Thesubjectmatter for this course has wide applications and so this course isa valuableelective for non-specialists.
MATH/CS248. Computer Methods inEngineering and Science (3,2). 4credits.
Programming in a high-level programming language such asBASIC or FORTRAN is taught as a basis for using the computer to solve problems in areas basic to numerical work in engineering and science. The prerequisite structure is designed to allowqualified non-majors to access numerical mathematics and mathematical modelingcourses.
Computational mathematics is becoming more important intraditionally "non-hard" sciences and social sciences. This provides an avenue for good students who have taken MATH 205-206 (Introductory Calculus I, II, 3 credits eachsemester) to take computational mathematics and mathematical modeling. This course is part of a package designed toinclude more types of students in numerical mathematics and mathematical modeling.
Syllabus:
(a) Mathematical preliminaries.
(b) Solution methods for non-linearequations.
(c) Convergence of solution methods.
(d) Solutions of systems of equations.
(e) Use of functions and procedures innumerical methods.
(f) Interpolation.
1. Lagrange and Newton interpolatingpolynomials.
2. Divided differences.
(g) Differentiation.
1. Richardson extrapolation
2. Local and global error analysis.
(h) Numericalintegration.
1. General Newton-Cotes methods.
2. Trapezoidal rule and Simpson's rule.
3. Romberg integration.
4. Local and global error withNewton-Cotes Methods.
(i) Solutionsto differential equations.
1. Euler and modified Euler solutions.
2. Runga-Kutta methods.
3. Multi-step methods.
(j) Curvefitting
Math 248 is a LEVEL I course and is required in themathematics major. The specificobjectives for the course are: 1. (a), (b), 2. (c), 3. (a), (b).
MATH 285. DataAnalysis. 4 credits.
Concepts of data analysis are developed through a study ofexperimental and survey design, distributions, variation, chance, sampling variation, computer simulation, bootstrapping, estimation and hypothesistesting using real data generated from classroom experiments and large databases.
Math 285 provides students a "hands-on,"calculus-based, highly computer-oriented approach to the introduction ofprobability and statistics. The subjectmatter and approach to the material is particularly suitable for students whohave an interest in the interaction of science and statistics.
Syllabus:
(a) DescribingData with STATGRAPHICS, SAS.
1. Univariate: histogram,stem and leaf, boxplot, mean (derived as least squaresestimate of mu) median,percentiles, stdev., etc.
2. Bivariate: scatterplot,lplot, mplot, correlation, least squares line,association vs causation.
(b) ProducingData by Sampling.
1. Terms: population, unit,sample, sampling frame, etc.
2. Need for sampling design.
3. Simple random sampling, selections ofSRS's.
4. Sampling variability, sampling error,sampling distribution.
5. Stratified random sampling.
(c) ProducingData by Experimentation.
1. Terms: experiment, units,variable, response variable, factor, treatment,design of experiment.
2. Need for experimental design.
3. Basic principles of experimentaldesign: comparison, randomization,replication.
4. Completely randomized design,randomized block design.
(d) Probability- the study of chance.
1. Introduction: randomphenomena, probability, prob. in statistical inference,basic ideas, applications.
2. Probability model, axioms of prob.,equally likely outcomes.
3. Counting principles: mult. rule, permutations, combinations,partitions.
4. Properties of probability, generaladdition rule, complements, conditionalprobability, multiplication rule,independence.
(e) DiscreteRandom Variables/Populations.
1. Random variables and theirdistributions.
2. Expected values of random variables andfunctions of random variables,properties of expectations.
3. Bernoulli populations and r.v.
4. The hypergeometric distribution.
5. The binomial distribution, Minitab.
(f) Continuous RandomVariables/Populations.
1. Cont. r.v.'s and their distributions.
2. Expected values of cont. r.v.'s.
3. The uniform dist.
4. The expo. dist.
5. The normal dist.
(g) Statisticsand Sampling Distributions.
1. Sample mean and variance.
2. Sampling dist. of the sample mean
3. Normal approx. to the bin. dist.
(h) Estimation.
1. Point estimators and properties
2. Confidence interval for mean: normaland non-normal pops.
3. Sample sizes for estimating means
(i) Hypothesistesting.
1. Basic concepts, logic of hypothesistesting, power, p-value, etc.
2. Hypothesis testing about a singlemean: normal and non-normalpopulations.
3. Hypothesis testing about two or moremeans: analysis of variance, multiplecomparison procedures.
Math 285 is a LEVEL I course designed for applications oriented students who have an appropriate background. This course offers entry to the remainder of the appliedstatistics courses and is an elective for students wishing to minor in statistics.
The specific objectives for the course are : S1. (a)-(g), S2. (e)-(h).
The subject matter of this course has wide application andso this course serves as an elective for several majors across campus.
Math 300. LinearAlgebra. 3 credits.
An introduction to linear algebra is developed through astudy of vector spaces, linear transformations, matrices, determinants,systemsof linear equations, eigenvalues and eigenvectors.
Math 300 is designed to begin the process of abstraction andthe development of proof. Basic definitionsand concepts are introduced and used to establish a basis for the understandingof factual information that is often taken for granted, such as the statement"a system of linear equations either has no solutions, exactly onesolution or infinitely many solutions." The subject matter of this course has relevance to almost all applications of mathematics and so this course is a valuable elective for non-mathematics majors who have a calculus background and level of mathematical maturity.
Syllabus:
(a) Systems of linear equations andmatrices.
(b) Determinants.
(c) Vectors in 2-space and 3-space.
(d) Vector spaces.
(e) Linear Transformations.
(f) Eigenvalues and eigenvectors.
Math 300 is a LEVEL II course and is a requirement in themathematics major. The specific objectives for the course are:
1. (a)-(d), 3. (i)-(k), 4. (f)-(i)
This course serves as an elective for any student wishing tominor in mathematics.
Math 310. ElementaryTheory of Numbers. 3 credits.
The theory of numbers is developed through a study of theproperties of integers and prime numbers, divisibility, congruence, residues and selected topics.
Math 310 is designed to begin the process of abstraction andthe development of proof. Basicdefinitions and concepts are introduced and used to establish a basis for theunderstanding of factual information that is often taken for granted, such asthe statement "an integer is divisible by three if and only if the sum ofit's digits is divisible by three." The subject matter of this course is particularly useful tomiddle andsecondary teachers and so this course is a valuable elective forstudents whowish to become teachers.
Syllabus:
(a) Preliminary considerations.
(b) Divisibility theory in the integers.
(c) Primes and their distribution.
(d) The theory of congruences.
(e) Fermat's theorem.
(f) Primitive roots and their indices.
Math 310 is a LEVEL II course and is an elective inthemathematics major. The specificobjectives for the course are: 1.(a)-(d)
This course is an elective in the teacher certification program and serves as an elective for any student wishing to minor inmathematics.
MATH 315. The RealNumber System. 3 credits.
The system of the real numbers is developed throughasystematic study of the natural numbers, integers, rationals, and irrationals.
Math 315 is designed to begin the process of abstraction andthe development of proof. Basicdefinitions and concepts are introduced and used to establish a basis for the understandingof factual information that is often taken for granted, such as the twostatements "the square root of 2 is not rational," or "between any two distinct numbers there is a rational number." The subject matter of this course isparticularly useful tosecondary teachers and so this course is a valuableelective for studentswho wish to become teachers.
Syllabus:
(a) Notation,logic, and sets.
(b) Relations.
(c) Binaryoperations.
(c) The naturalnumber system.
(d) Order andcancellation.
(e) Well-ordering.
(f) One-to-onecorrespondences and counting.
(g) Theintegers.
(h) Ordering theintegers.
(i) Notationfor the integers.
(j) Therational numbers.
(k) Ordering therational numbers.
(l) Someconcluding remarks about the rational numbers.
(m) An intuitivelook at the real numbers.
(n) Sequences.
(o) The realnumbers.
(p) Order.
(q) Completeness(optional).
(r) Dedekindcuts (optional).
(s) The Peanoaxioms (Optional).
Math 315 is a LEVEL II course and is an elective inthemathematics major. The specificobjectives for the course are: 1. (a)-(d).
This course is an elective in the teacher certification program and serves as an elective for any student wishing to minor inmathematics.
MATH 318. Introduction to Probability and Statistics. 3 credits.
The theories of probability and statistics are developed ina course that introduces the student to descriptive statistics, counting, probability, random variables, sampling distributions, estimation, regression and correlation.
Math 318 is a calculus based course that is required ofmathematics majors. It isa coursedesigned to lead into the applied statistics courses and to the capstone statistics course Math 426-427. This isa course that lays the foundation for the theory of statistics.
Syllabus:
(a) Introduction to the nature ofprobability and statistics.
(b) Probability and counting.
1. Probability measure.
2. Permutations.
3. Combinations.
4. Conditional probability.
5. Independence.
(c) Discreterandom variables, distributions and moments.
1. Bernoulli.
2. Binomial.
3. Geometric.
4. Negative binomial.
5. Poisson.
6. Hypergeometric.
(d) Continuousrandom variables, distributions and moments.
1. Uniform.
2. Exponential.
3. Gamma.
4. Normal.
(e) Multivariateprobability distributions.
1. Joint, marginal and conditional.
2. Independence.
3. Expectations.
4. Covariance.
(f) Samplingand statistics.
1. Sampling distributions of the samplemean and sample variance.
2. Central limit theorem.
(g) Point and interval estimation of thepopulation mean (including proportion)and population variance.
(h) Testing the hypothesis involving thenormal and related distributions.
Math 318 is a LEVEL II course that is a required course ofall mathematics majors. The specificobjectives of the course are: 2. (e) 3. (m), (n) S1. (a)-(d), (i), (l).
MATH 321. Analysisof Variance and Experimental Design. 3credits.
Basic concepts in statistics and basic statisticaltechniques are introduced and reinforced through the study of applications instatistics. The topics covered includeestimation, test of hypothesis, analysis of variance and selected topics inexperimental design.
The design of an experiment refers to the choice oftreatments and the manner in which experimental units or subjects are assignedto the treatments in a scientific study. Selection of an appropriate design is crucial in avoiding confoundingresults and minimizing experimental error. Math 321 covers some basic experimental designs with correspondingmodelsand analyses. This course isanimportant course for a variety of students in the empirical sciences.
Syllabus:
(a) Introduction/Review.
1. Confidence interval for µ1=µ2 (equal variance).
2. Test of H0: µ1=µ2 (equal variance).
3. Test of H0: s 12=s2 2 (Bartlett‑Box).
4. Test of normality (Shapiro‑Wilk,Normal plot).
5. Test of outliers (Dixon, Boxplot).
6. Introduction to SAS.
(b) One‑wayANOVA: fixed effects.
(c) Hierarchicaland nested designs.
(d) Two factorANOVA: fixed effects.
1. Two‑way factorial.
2. Randomized complete block design.
(e) Three factorANOVA: fixed effects.
1. Three‑way factorial.
2. Latin square design.
(f) Variableeffects models.
1. Random models.
2. Mixed models.
3. Variance components.
(g) Repeatedmeasures designs.
1. Within subjects ANOVA.
2. Split plot design.
3. Cross‑over design.
Math 321 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors.
The specific objectives for this course are: S2. (a)-(h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
Math 322. AppliedLinear Regression. 3credits.
Basic concepts and methods in regression analysis are studied through the application of linear regression models to real-lifesituations.
Regression analysis is an area of statistics that deals withmethods for quantifying the relationship between a dependent variable and oneor more independent variables for the purposes of description andprediction. For example, a collegeadmissions officer might be interested in predicting the gpa of a prospectivefreshmen based on variables such as high school gpa, rank in class, amount ofextracurricular activity, etc. Math 322covers the basic concepts of regression models andmodel building. This coursewould be beneficial to anyoneplanning on going into a quantitative field.
Syllabus:
(a) Introductionto regression analysis.
(b) Populations,samples, and probability distributions.
(c) Basicstatistical inference.
(d) The simplelinear regression model.
(e) Inference insimple linear regression.
(f) Theassumptions behind regression analysis.
(g) Multipleregression.
(h) Modelbuilding.
Math 322 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors.
The specific objectives for this course are: S2. (a)-(h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
MATH 323. Exploratory Data Analysis. 3 credits.
Exploratory data analysis is introduced through a study ofbox plots, stem-and-leaf displays, re-expression, medial polish, smoothing androbust regression. Applications andinteractive computing are an integral part of the course.
The methodology in this class provides a student with aninformal, yet systematic way to examine the structure of virtually anydataset. The methods presentedin Math 323have broad application in the physical, biological, social andmanagementsciences.
Syllabus:
(a) Introduction.
(b) Displayingunivariate data.
1. Stem and leaf display.
2. Letter value display.
3. Boxplot.
4. Re-expression.
5. Quantile plot.
6. Rootogram.
(c) Describingmultivariate data.
1. x-y plotting, re-expression.
2. Resistant lines.
3. Smoothing.
4. Coded tables.
5. Median polish.
Math 323 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors.
The specific objectives for this course are: S2. (b), (c),(e), (h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
MATH 324. AppliedNonparametric Statistics. 3 credits.
The principles of nonparametric statistics are introduced through a study of the methods used to analyze non-normal populations. The methods include binomial tests,contingency tables, useof ranks, Kolmogorov-Smirnov type statistics and otherselected topics.
Assessing the reliability of conclusions drawn fromstatistical methods involves the selection of an appropriate probability modelfor the phenomenon under study. Traditionally normal models have been assumed even though the phenomenonunder study does not have exactly the normal distribution. Finding probabilities for the true model ora more reasonable model may be difficult. Alsothe assumption of normality leads to well-studied"parametric" methods suchas the "t test" or the "Ftest". Nonparametric statisticalmethods do not make the assumption of normality. They are based on reasonable if not exact models whoseprobabilities can be calculated using simple and unsophisticated methods. This course would be beneficial to studentsin the biological and social sciences.
Syllabus:
(a) Comparisonof two treatments.
1. The Wilcoxon test.
2. The Siegel-Tukey test.
3. The Smirnov test.
4. Estimation of treatment effect.
(b) Comparisonof more than two treatments.
1. The Kruskal-Wallis test.
2. 2xt contingency tables.
(c) Randomizedcomplete blocks.
1. The Friedman test.
2. The Cochran test.
3. The McNemar test.
(d) Tests ofrandomness and independence.
1. Testing against the trend.
2. Testing for independence.
3. sxt contingency tables.
Math 324 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors. Thespecific objectives for this course are: S1. (a), S2. (a), (h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
MATH 325. SurveySampling Methods. 3 credits.
The theory and practice of sampling are introduced through astudy of stratified random samples, simple random samples, cluster sampling, estimating sample size, ratio estimates, subsampling, two-state samplingandanalysis of sampling error.
Sampling is a fundamental stage in virtually everystatistical procedure and is primary to survey research. As such, a person who participates in thepractice of sampling should have an understanding sufficient to give a unifiedbasis to the sampling methods. Math 325is an important course for students in education and the social, medical,biological and management sciences.
Syllabus:
(a) Introduction.
(b) Review ofstatistical concepts.
(c) The samplingproblem.
(d) Somesampling designs.
1. Simple random sampling.
2. Stratified random sampling.
3. Ratio, regression, and difference estimation.
4. Systematic sampling.
5. Cluster sampling.
6. Two-stage cluster sampling.
(e) Estimatingthe population size.
Math 325 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors.
The specific objectives for this course are: S2. (a)-(h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
MATH 326. Statistical Quality Control. 3credits.
The uses and concepts of probability and sampling procedures are introduced through a study of acceptance sampling by attributes and by variables, Shewhart concepts ofprocess control, control chart process, capability studies, reliability, lifetesting and the design of sampling plans.
Quality control is a subject of interest and of practical use to any major who will become involved in managing, designing or controlling a manufacturing process. Industrial quality control is an important aspect of efficiency in manufacturing and manyindustries require personnel to be trained in this area. Math 326 is an important course for avariety of majors whoare interested in an industrial career.
Syllabus:
(a) Introduction to quality assurance andquality control.
(b) Review of probability and statistics.
(c) Introduction to control charts.
(x, R, b, and ocharts)
(d) Control chart patterns.
(e) Process capability studies.
(f) Fundamental concepts in acceptance sampling.
(g) Lot-by-lot acceptance sampling byattributes.
(h) Acceptance sampling by variables.
(i) Reliability and life testing.
(j) A quality control program.
Math 326 is a LEVEL II course designed for studentswho wishto minor in statistics. It serves as anelective for mathematics majors.
The specific objectives for this course are: S2. (a)-(h).
The subject matter of this course has broad application tomany disciplines and can be used as an elective to complete the B.S.requirement in mathematics.
MATH 435. Introduction to Topology. 3 Credits.
The elementary concepts of topology are developed through astudy of metric spaces, limits, continuous maps and homeomorphisms,connectedness, compact topological spaces and applications.
Math 435 is designed to continue the process of abstraction and the development of proof. Basicdefinitions and concepts are introduced and used to establish a basis for theunderstanding of factual information that is often taken for granted, such asthe statement "the continuous image of a connected segment isconnected." The subject matter ofthis course is particularly useful tostudents who wish to pursue graduatestudy in mathematics or undertake a researchproject in pure mathematics.
Syllabus:
1. Topological Spaces and subspaces
2. Continuity and homeomorphisms
3. Product spaces
4. Connectedness
5. Compactness
6. Hausdorff spaces
7. Metric spaces
Math 435 is a LEVEL III course and is an elective in themathematics major. The specific objectives for the course are: 1. (a)-(d)
This course is an elective in the pure concentration andserves as an elective for any student wishing to minor in mathematics.
MATH 336. Elementary Differential Equations. 3 credits.
The theory of elementary differential equations is developed through a study of techniques for obtaining, analyzing and graphing solutions to differential equations, with emphasis on first and second order equations.
Math 336 is a course designed to give students theopportunity to understand how the ideas developed in calculus may be applied towidely diverse systems which undergo change.
Syllabus:
(a) Techniquesthat follow directly from the calculus.
(b) A theory for second order linearequations.
(c) Power seriesand other numerical methods.
(d) The Picarditeration and its consequences.
Math 336 is a LEVEL II course that is required of all mathematics majors. The subject matterof this course has wide application and so it serves as an elective for othermajors.
The specific objectives for the course are: 1. (a)-(e), 2.(b), (c), (d) 3. (e),(l).
MATH 337. AppliedCalculus. 3 credits.
Applications of calculus via the subject of vector analysis are introduced through astudy of line and surface integrals, Green's theorem, the divergence theoremand Stokes' theorem and potential theory.
Math 337 is designed to give students exposure toapplications from calculus to classicalanalysis and the physical sciences.
Syllabus:
(a) Vector analysis
1. Multivariate functions.
2. Coordinate systems.
(b) Multivariatecalculus.
1. Line and surface integrals.
2. Green's theorem.
3. The divergence theorem and Stokes'theorem.
4. Potential theory.
(c) Selectedtopics.
Math 337 is a LEVEL II course which serves as an elective inthe mathematics major or minor. It isalso an elective in the concentration in computational and appliedmathematics. The specific objectivesfor the course are: 1. (a)-(e), 2. (c), 3. (g), 4. (d), (i).
Thetopics in this course have broad applications and so this course servesas anelective for a variety of majors.
MATH 340. Mathematical Modeling I. 3credits.
Matrices and computers are used to model problems in thephysical, biological, social, and management sciences. Linear and non-linear optimization methodswill be stressed, along with computervisualization.
The course is designed to demonstrate to non-majorsandmajors in mathematics how mathematics, specifically matrices, and computerscanbe used to model real world situations.
Mathematical modeling is increasingly becoming moreimportant to many disciplines. Thiscourse provides an entry to the area of mathematical modeling for students fromvarying disciplines. It is the first course of a year sequence in mathematical modeling that stresses computation and visualization and will help students perform research and find challenging employment after graduation. MATH 340is part of a package that provides a wide range of students the opportunity tostudy mathematical modeling.
Syllabus:
(a) Systems oflinear equations.
1. Solvingmatrix equations.
2. Eigenvaluesand eigenvectors.
3. LinearEquations with constraints.
4. Applications of these methods,including differential equations.
(b) Systems ofnonlinear equations.
1. Multivariatecalculus.
2. Taylorpolynomials of one and two variables.
3. Newton-Raphsonmethods.
4. Optimizationtechniques.
5. Optimizationtechniques with constraints.
6. Applicationsof these methods.
Math 340 is a LEVEL II course which serves as an elective inthe mathematics major or minor. It isalso an elective in the concentration in computational and appliedmathematics. The specific objectivesfor the course are : 1. (a)-(e), 3.(a), (b), (e), (i), 4. (c).
The topics in this course have broad applications and sothis course serves as an elective for a variety of majors.
MATH 341. Mathematical Modeling II. 3credits.
Differential equations and elementary probability and statistics are used to develop and analyze both continuous and discrete models that arise in the application of mathematics to the physical, biological, social and management sciences.
The course is designed to demonstrate to non-majorsandmajors in mathematics how mathematics, specifically differential equationsandstatistics, can be used to develop both continuous and discrete modelsof realworld situations.
Applications in mathematics have always involved the building and analysis of models of perceived reality. An increasing number of disciplines are beginning to more widely use mathematical modeling. MATH 341 ispart of a package that provides a wide range of students the opportunity tostudy mathematical modeling.
Syllabus:
(a) Models foraxiomatic systems.
1. Models for the numbers.
2. Models for geometry.
(b) Analyzinggiven models.
1. Making models to which calculusapplies.
2. Models given in the textbook.
(c) Makingmodels straight from context.
1. Small group project.
2. Large group project.
Math 341 is a LEVEL II course which serves as an elective inthe mathematics major or minor. It isalso an elective in the concentration in computational and appliedmathematics. The specific objectivesfor the course are : 1. (a)-(e), 3.(a), (b), (e), (i), 4. (c).
The topics in this course have broad applications and sothis course serves as an elective for a variety of majors.
Math 352-353. Discrete Mathematics. 3 credits each semester.
The flavor of discrete structures and proof theory involving discrete processes are studied through an investigation of logic, set theory, relations and functions, counting, recurrence relations, Boolean algebras and functions, graphs andtrees.
Math 352 is designed to begin the process of abstraction andthe development of proof. Basicdefinitions and concepts are introduced and used to establish a basis for theunderstanding of factual information that is often taken for granted.
Discrete mathematics describes processes that consist of asequence of individual steps. Calculusinvolves the study of continuously changing phenomena. The ideasof calculushave been and are fundamental to science and technology. The ideas of discrete mathematics, thoughmany have been studied for over two hundred years, have become fundamental toscience and technology specifically related to the computer and the computerage.
These courses provide an upper level sequence blending applications and theory. Itis designedfor mathematics majors and is recommended for those seeking teacher certification. Both the Mathematical Association of America and the National Council of Teachers of Mathematics includediscrete mathematics among their recommended standards. The most recent NCATE review also recommendssuch a course for students seeking teacher certification. In addition to the certification function,discrete mathematics serves as an upper level elective for mathematics majorsand as a transition course to prepare students for theoretical studies in theircapstone experience.
Syllabi:
1) Math 352 (a) Logic.
1. Basic connectives.
2. Truth tables.
3. Logical equivalence.
4. Arguments.
5. Quantification.
(b) Operations and laws ofset theory.
(c) Induction.
(d) Relations and functions.
1. One-to-oneand onto functions.
2. Inverse relations and functions.
3. Compositions.
4. Equivalence relations and partitions.
5. Partial orderings.
6. Finite state machines.
(e) Counting.
1. Permutations and combinations.
2. inclusion and exclusion principles.
3. Generating functions.
(f) Recurrence relations.
2) Math 353 (a) Graphtheory.
1. Isomorphisms
2. Euler trails and circuits.
3. Planar graphs.
4. Hamiltonian paths and circuits.
(b) Trees.
1. Rooted trees.
2. Sorting algorithms.
3. Spanning trees.
4. Weighted trees.
5. Optimization.
(c) Boolean algebras and switching functions.
(d) Selected topics
1. Coding theory (optional).
2. Combinatorics (optional).
3. Computational complexity (optional).
Both Math 352 and Math 353 are LEVEL II courses andareelectives within the mathematics major. The specific objectives of the courses are: 1. (a)-(e), 3. (a),(f), 4.(c).
These courses cover material that is beginning to appear inthe high school curriculum and so these courses are valuable electivesforthose who wish to get a teaching certification.
MATH 360. Complex Variables and its Applications. 3 credits.
The subject of complex variables is developed through astudy of the algebraic properties of the complex numbers, analytic functions, harmonic functions, mappings of elementary functions, contour integration, series, residues and poles and conformal mappings. Special emphasis is placed on computation and application to fluid and heat flow.
Math 360 is designed to provide students entry level theoryand applications of classical complex analysis. The material covered in Math 360 has applications in the physical sciences to such phenomena as air glow over aircraft wings and heat flowthrough different laminae. Studentsmajoring in the physical sciences who have studied calculus may take thiscourse as an elective.
Syllabus:
(a) Algebraic properties of the complexnumbers.
(b) Analytic and harmonic functions.
(c) Heat and fluid flow problems.
(d) Mappings of elementary functions.
(e) Contour integration.
(f) Partial solutions to heat and fluidflow problems.
(g) Series, residues and poles.
(h) Applications to improper Reimann integralsand Laplace and Fouriertransforms.
(i) Conformal mappings.
(j) Applications in heat and fluid flowproblems.
Math 360 is a LEVEL II course which serves as an elective inthe mathematics major or minor. It isalso an elective in the concentration in computational and appliedmathematics. The specific objectivesfor the course are : 1. (a)-(e), 2.(b), (c), 3. (d), 4. (a).
The topics in this course have broad applications and sothis course serves as an elective for a variety of majors.
MATH 387. Fourier Analysis and Partial Differential Equations. 3 credits.
Fourier analysis and partial differential equationsareintroduced through a study of elementary applied partial differentialequationssuch as the heat equation, Laplace's equation and the wave equation. Fourier series and boundary value problems are also introduced andstudied. Math 387 includes the development of both the theory of thesubject and problem solving skills.
Syllabus:
(a) "Usual"three operations.
1. Potentialoperator.
2. Diffusionoperator.
3. Waveoperator.
(b) First orderpartial differential equations.
(c) Classificationof 2nd order partial differential equations.
(d) "Usual"problems and boundary conditions.
(e) "Usual"Solution Methods.
1. Separationof variables/Fourier series.
2. Green'sfunctions.
3. Variationalmethods.
4. Numericalmethods.
(f) Mathematicaltools.
1. Divergencetheorem.
2. Inequalities.
3. Convergencetheorems.
(g) Selectedtopics.
Math 387 is a LEVEL II course which serves as an elective inthe mathematics major or minor. It isalso an elective in the concentration in computational and applied mathematics.
The specific objectives for this course are: 1. (a)-(e), 3.(b).
MATH 410-411. Advanced Calculus II and II. 3 credits eachsemester.
A complete development of the theory of calculus isundertaken through the study of limits, continuity, differentiation, sequences,series, integration and selected topics.
Math 410-411 is a two semester sequence that forms a capstonecourse for mathematics majors. Allmathematics majors, except those seeking teacher certification, are required tocomplete either Math 430-431 or Math 410-411. The thrust of the course is to engage the student in proving theoremsand to give them sufficient background in an area to begin to understand thebeauty of a complete theory and how it is put together.
At least one capstone course (Math 410-411 or Math 430-431) is required of all mathematics majors.
Syllabi:
1) Math 410 (a) Limits through continuity.
(b) Intermediate and extreme value theoremsfor continuous functions.
(c) Heine-Borel theorem.
(d) uniform continuity.
(e) derivatives.
Math 410 is a LEVEL III course and is required of all mathematics majors. The specific objectives of the course are: 1. (a)-(e), 4. (a)-(c)
2) Math 411 (a) l'Hôpital's rule.
(b) Taylor's theorem.
(c) Definition of the integral.
(d) Existence of the integral.
(e) Properties of the integral.
(f) Countable sets.
(g) Sets of measure zero.
(h) Lebesgue's theorem.
(i) Sequences and series of functions.
(j) Uniform convergence
(k) Interchange of limits.
Math 411 is a LEVEL III course and is the completion of Math410. This course serves as an electivein the mathematics major and together the sequence forms acapstone course. Thespecific objectives for the course are: 1. (a)-(e), 4.(d), (e).
MATH 415. History ofMathematics. 3 credits.
Topics in the history of mathematics from ancient times tothe present are incorporated in the curriculum to develop an appreciation ofthe place of mathematics in the general culture and to give an overview of thehistorical development of the discipline of mathematics.
Math 415 is designed to help students of mathematics developboth a broader and deeper view of the discipline. The subject matter of this course is especially appropriate forstudents who wish to teach mathematics.
Syllabus:
(a) Major themes.
1. Foundations of mathematics.
2. Infinitesimal analysis.
3. Development of the real number system.
4. Limit concept.
5. Computing devices and machines.
(b) Topicsintegrated into these themes.
1. Axiomatics, consistency, independenceand equivalence.
2. Ancient numeration systems and basesother than ten.
3. The discovery of incommensurables.
4. Euclid -- books I and V.
5. Archimedes' quadrature and method.
6. Cavalieri's indivisibles, Roberval'squadrature of the cycloid, infinitesimalmethods.
7. Cardano and the "Cossic" art(the cubic).
8. The impossibility of the quintic.
9. Galois theory.
10. The three classical problems.
11. Tally sticks and the abacus.
12. Dedekind cuts.
13. Peano postulates.
14. Cantor's transfinite arithmetic.
15. The parallel postulate.
16. Non-Euclidean geometries.
17. Gauss construction of the regular n-gons.
18. Newton and Leibnitz and the lack of rigorin analysis.
19. Non-standard analysis.
20. Boolean algebra.
21. Quaternians and electromagneticradiation.
22. The role of computers in WW II.
23. Artificial intelligence.
24. Independence of the axiom of choice andthe continuum hypothesis from theaxioms for set theory.
25. The loss of certainty in mathematics.
Math 415 is a LEVEL III course and serves as an elective forall mathematics majors. The specificobjectives of the course are: 1. (a)-(e)
MATH 420. Foundations of Euclidean Geometry. 3 credits.
The structure and content of Euclidean geometry is studied from an advanced standpoint.
Math 420 is a course designed to provide students asophisticated exposure to Euclidean geometry. The subject matter of this course is particularly appropriate forstudents who wish to become secondary teachers. At least one of two geometry courses (Math 420, Math 475) isrequired of all mathematics majors who seek secondary teaching certification.
Syllabus:
(a) The incidence axioms and the parallelpostulate.
(b) The cartesian model.
(c) Vector models.
(d) Line segments.
(e) Rays.
(f) Angles.
(g) Congruence.
Math 420 is a LEVEL III course and is an elective in themathematics major. The specific objectives of the course are : 1. (a)-(e).
Math 421. AppliedMultivariate Statistical Analysis. 3 credits.
Multivariate statistical analysis is developed through astudy of several topics, including canonical correlation, clustering, discriminant analysis, factoranalysis, multivariate analysis of variance, multiple regression,multidimensional scaling and principal components analysis.
Math 421 provides students with methods of analysisthat arean integral part ofthe standardarsenal of analytic tools available to applied statisticians. The course is designed for students who havehad a previousstatistics course (Math 321 or Math 322) as a prerequisite. The subject matter of this course is ofparticular importance to social scientists, biologists and managementscientists who use quantitative methods of analysis.
Syllabus:
(a) Univariate techniques using matrixnotation.
(b) Principal Components analysis.
(c) Cluster analysis.
(d) Discriminant analysis.
(e) Multivariate analysis of variance.
(f) Multiple regression.
(g) Canonical correlation analysis.
(h) Loglinear models.
Math 421 is a LEVEL III course which serves as an elective in the mathematics major or minor. Itis also an elective in the concentration in computational and appliedmathematics.
The specific objectives for the course are: S2. (a)-(h).
Math 423. Stochastic Processes. 3 credits.
Stochastic Processes are developed through a study of sequences and classes of random variables such as Markov chains, branching processes, the Poisson process, queuing systems and renewal processes.
Math 423 is designed to provide students in the physical, biological, social and management sciences the opportunity to study moresophisticated statistical processes.
Syllabus:
(a) Preliminariesin probability.
(b) Markovchains.
1. Transition probabilities and theChapman-Kolmogorov equation.
2. Classification of states.
3. Limiting probabilities.
(c) Branchingprocesses.
1. Extinction probabilities.
2. Total progeny.
(d) The Poissonprocess.
1. Construction of a Poisson process.
2. Waiting time and inter-event timedistributions.
3. Compound Poisson processes.
(e) Queuingsystems.
1. Single-server queuing systems.
2. Multiple-server systems.
(f) Renewal processes.
1. Limit theorems.
2. Generalizations.
3. Variations.
(g) Applications.
Math 423 is a LEVEL III course designed for students whowish to minor in statistics. It servesas an elective for mathematics majors. The specific objectives for this course are: S1. (a)-(d), (n).
The subject matter of this course has broad application tomany disciplines.
MATH 424. Statistical Decision Theory. 3credits.
The development and use of probability and statistics forstrategic decision-making are the focus of this course. The topics studied include decision theoryflow diagrams, analysis of risk and risk aversion, utility theory, Bayesianstatistical methods, the economics of sampling, sensitivity analysis andcollective decision-making.
Math 424 is designed to provide students who major or minorin statistics the opportunity to study sophisticated and comprehensive statistical decision theories.
Syllabus:
(a) Introduction/Reviewof probability.
(b) Loss andrisk functions.
(c) Admissibility.
(d) Geometricalsolutions.
(e) Minimaxrules.
(f) Bayesrules.
(g) Estimationand hypothesis tests.
(h) Sequentialdecision problems.
(i) Sensitivityanalysis.
Math 424 is a LEVEL III course designed for students whowish to minor in statistics. It servesas an elective for mathematics majors. The specific objectives for this course are: S1. (j), (o), (p).
The subject matter of this course has broad application tomany disciplines.
MATH 426-427. Probability and Mathematical Statistics I and II. 3 credits each.
The theories of probability and statistics are developed through a systematic study of probability spaces, random variables, discrete and continuous probability distributions, mathematical expectation, moment generating functions, moments of linear combinations of random variables, sampling theory and distributions, theory and applications of estimationandhypothesis testing, regression and correlation and analysis of variance.
Math 426-427 is a two semester sequence that forms a capstone course in the statistics offerings. This is a required sequence for mathematics majors who minor instatistics. The subject matter of thesecourses is particularly suited to persons who wish to go on to graduate studyin statistics or to employment at an entry level statistics position inbusiness, industry or government.
Syllabi:
1) Math 426 (a) Probability.
(b) Random variables and random vectors.
(c) Expectation.
1. Special expectations.
2. Moment generating functions.
3. Conditional expectation.
(d) Examples of probability distributions.
1. Binomial and Poison.
2. Distributions associated with thenormal.
(e) The bivariate normal distribution.
(f) Asymptotic distributions.
1. Convergence in distribution.
2. Central limit theorem.
Math 426 is a LEVEL III course and is an elective course forall mathematic majors. The specificobjectives of the course are: S1. (a)-(d), (h)-(j), (p).
2) Math 427 (a) Estimation
1. Maximum likelihood estimators.
2. Unbiased estimators.
3. Consistent estimators.
(b) Confidence intervals and tests.
1. Pivotal quantities.
2. Testing statistical hypotheses.
3. Power.
(c) Optimal tests.
1. Most powerful tests.
2. Likelihood ratio tests.
(d) Sufficient statistics.
1. Factorization criteria.
2. Minimal and complete sufficiency.
(e) Linear statistical models.
1. Linear regression.
2. Analysis of variance.
(f) Basin statistics.
1. Confidence intervals.
2. Hypothesis tests.
Math 427 is a LEVEL III course and is an elective course forall mathematic majors. The specificobjectives of the course are: S1. (a)-(d), (h)-(j), (p).
MATH 430-431. Abstract Algebra I and II. 3 credits each.
The basic theory of abstract algebra is developed through asystematic study of algebraic structures including groups, rings and fields.
Math 430-431 is a two semester sequence that forms a capstone course for mathematics majors. All mathematics majors, except those seeking teacher certification, arerequired to complete either Math 430-431 or Math 410-411. The thrust of the course is to engage thestudent in proving theorems and to give them sufficient background in an areato begin to understand the beauty of a complete theory and how it is puttogether.
Syllabi:
1) Math 430 (a) Sets and relations.
(b) Equivalence relations.
(c) Congruences.
(d) Rings
1. Definition and examples.
2. Commutativity.
3. Identity.
4. Units.
5. Homomorphisms and isomorphisms.
6. Quotient rings.
7. Order.
8. The integers and the divisionalgorithm.
9. Elementary number theory.
(e) Integral domains.
(f) Fields.
(g) Fields of quotients.
(h) Factorization and polynomial rings.
Math 430 is a LEVEL III course required of all mathematics majors. The specific objectives of the course are: 1. (a)-(e), 4. (j),(k).
2) Math 431 (a) Ideals and Field extensions.
(b) Groups.
(c) Finite groups.
(d) Finite abelian groups.
Math 431 is a LEVEL III course and is the completion of Math430. This course serves as an electivein the mathematics major and together the sequence forms acapstone course. Thespecific objectives for the course are: 1. (a)-(e), 4.(j), (k).
MATH 448-449. Numerical Mathematics and Computer Applications. 3 credits each semester.
The subject of numerical mathematics is developed through astudy of numerical solutions and error analysis of typical problems such as;finding zeros of nonlinear functions, solving systems of linear and nonlinear equations, interpolation, approximation, integration, solving ordinarydifferential equations, optimization and Monte Carlo methods.
Math 448 and Math 449 are designed to give studentsanopportunity to study in-depth applications of mathematics and to learnnumericalcalculus. They introduce the students to a study of usingnumerical methodsto approximate solutions to equations and to implement themon the computerusing a high level computing language and visualization andgraphics packages. This course isuseful to students in any discipline who are using computer models to simulateproblems of interest.
Syllabi:
1) Math 448 (a) Numberssystems, convergence, stability, error analysis.
(b) Zeroes of functions of one variable.
(c) Interpolating polynomials - Vandermonde,Lagrange, Newton, Taylor.
(d) Numerical differentiation.
(e) Numerical integration.
(f) Systems of linear equations.
(g) Systems of non-linear equations.
Math 448 is a LEVEL III course which is an electivein themathematics major and minor programs and in the computational and applied mathematics concentration. The specificobjectives for the course are: 1. (a)-(e), 2. (c), 3. (a), (b), (i).
Taken with Math 449, the sequence forms a capstone course for students interested in applied mathematics.
2) Math 449 (a) Numericalmethods for approximating solutions to ode's.
(b) Numerical methods for approximatingsolutions to pde's.
Math 449 is a LEVEL III course which is an electivein themathematics major and minor programs and in the computational and applied mathematics concentration. The specificobjectives for the course are: 1. (a)-(e), 2. (c), 3. (a), (b), (i).
Taken with Math 448, the sequence forms a capstone course for students interested in applied mathematics.
MATH 448-449. Numerical Mathematics and Computer Applications. 3 credits each semester.
The subject of numerical mathematics is developed through astudy of numerical solutions and error analysis of typical problems such as;finding zeros of nonlinear functions, solving systems of linear and nonlinear equations, interpolation, approximation, integration, solving ordinary differential equations, optimization and Monte Carlo methods.
Math 448 and Math 449 are designed to give studentsanopportunity to study in-depth applications of mathematics and to learnnumericalcalculus. They introduce the students to a study of usingnumerical methodsto approximate solutions to equations and to implement themon the computerusing a high level computing language and visualization andgraphics packages. This course isuseful to students in any discipline who are using computer models to simulateproblems of interest.
Syllabi:
1) Math 448 (a) Numberssystems, convergence, stability, error analysis.
(b) Zeroes of functions of one variable.
(c) Interpolating polynomials - Vandermonde,Lagrange, Newton, Taylor.
(d) Numerical differentiation.
(e) Numerical integration.
(f) Systems of linear equations.
(g) Systems of non-linear equations.
Math 448 is a LEVEL III course which is an electivein themathematics major and minor programs and in the computational and applied mathematics concentration. The specificobjectives for the course are: 1. (a)-(e), 2. (c), 3. (a), (b), (i).
Taken with Math 449, the sequence forms a capstone course for students interested in applied mathematics.
2) Math 449 (a) Numericalmethods for approximating solutions to ode's.
(b) Numerical methods for approximatingsolutions to pde's.
Math 449 is a LEVEL III course which is an electivein themathematics major and minor programs and in the computational and applied mathematics concentration. The specificobjectives for the course are: 1. (a)-(e), 2. (c), 3. (a), (b), (i).
Taken with Math 448, the sequence forms a capstone course for students interested in applied mathematics.
Math 475. Fundamental Concepts of Geometry. 3 credits.
The foundations of geometry are developed through astudy ofthe origins, axioms, proofs and selected topics from incidence geometry.
Math 475 is a course designed to provide students asophisticated exposure to the axiomatic development of geometry. The subject matter of this course isparticularly appropriate for students who wish to become secondaryteachers. At least one of two geometrycourses (Math 420, Math 475) is required of all mathematics majors who seeksecondary teaching certification.
Syllabus:
(a) Axioms for selected finite geometries.
(b) The Pappus, Desargues and Fanoconfigurations.
(c) Axioms for Euclidean geometry.
(d) Transformations.
(e) Isometries.
(f) Similarities.
(g) Convexity.
(h) Euclidean geometry of the polygon andcircle.
(i) The theorem of Menelaus and itsconverse.
(j) The theorem of Ceva and its converse.
(k) The axioms of Hilbert.
(l) The axioms of Birkhoff.
(m) logical considerations.
(n) Geometric constructions.
Math 475 is a LEVEL III course and is an elective in themathematics major. The specific objectives of the course are : 1. (a)-(e).
This course provides an introduction to mathematical modeling, and in particular
several mathematical topics with particular applications to environmental
issues. A laboratory component is included. See also MATH 103
Topics:
1. Representing functions in symbolic, numerical, and graphical
form
2. Mathematical Models
3. Linear Functions
4. Exponential Functions
5. Power Functions
6. Polynomial Functions
7. Regression analysis
8. Sequences
9. Growth and Decay
10. Difference Equations
Math 103 is a LEVEL I course and satisfies the liberal studies requirement in mathematics. Thespecific objectives for the course are: 1. (a)-(e)