BS, Mathematics Fairmont State University, Lecture notes of Calculus

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BS, Mathematics

Fairmont State University

5 Year Program Review

Submitted Spring 2014

BS, Mathematics

Executive Summary for Program Review

(not to be more than 2-3 pages)

Name and degree level of program Mathematics – Bachelor of Science Degree Mathematics Education – Bachelor of Arts Degree 5-Adult Certification 5-9 Certification

External reviewer(s) NCATE (National Council for Accreditation of Teacher Education) Note: Although not all Math students are Math Education Majors, programmatic assessment occurs in courses common to both degrees.

Synopses of significant findings, including findings of external reviewer(s) The recommendation of the 2009 State Program Review Committee was to continue the Mathematics Program. NCATE recognized the program with full accreditation through 2018. Our program design is supported by guidelines from the American Mathematical Society. The program demonstrates a successful approach to sustainability, viability and assessment.

Plans for program improvement, including timeline No improvements necessary as a result of this review.

Identification of weaknesses or deficiencies from the previous review and the status of improvements implemented or accomplished NCATE did not find any weaknesses or deficiencies.

Five-year trend data on graduates and majors enrolled According to the National Center for Educational Statistics, undergraduate Math Degrees account for less than 1% of the total number of bachelor degrees awarded. Over the last five years the Fairmont State Mathematics Department has averaged approximately 8 straight Math Degrees and 11 total Math and Math Ed. Degrees awarded. This is 1.2% and 1.8 % respectively of the average number of bachelor degrees awarded by FSU in the four years between 2009 and 2012 according to the Fairmont State University Institutional Compact data, 2007-2012. Hence, our percentage of graduates is greater than the national average.

Summary of assessment model and how results are used for program improvement

The Mathematics program utilizes a departmental continuous improvement plan to meet institutional assessment needs. The continuous improvement plan consists of course assessment, programmatic assessment, and program modifications that are determined

 - Submitted Spring 5 Year Program Review 

• Approval Sheet/Signatures ································································································· Table of Contents
• Executive Summary·············································································································
• Catalog Description ·············································································································
• VIABILITY ·····························································································································
  • Enrollment Information ··························································································
    • Applications·································································································
    • Program Courses ·························································································
    • Success Rates of Program Courses ···························································
    • Service Courses ·························································································
    • Success Rates of Service Courses ······························································
    • Off Campus Courses ··················································································
    • Cost Per Student/Credit Hour ···································································
  • Liberal Studies Requirements ···············································································
  • Assessment Requirements····················································································
  • Adjunct Use ···········································································································
  • Graduation/Retention Rates·················································································
• ADEQUACY ························································································································
  • Program Requirements ·························································································
  • Faculty Data ··········································································································
  • Accreditation/National Standards ········································································
• NECESSITY ·························································································································
  • Placement and Success of Graduates ···································································
• CONSISTENCY WITH MISSION ···························································································
  • Relationship with Other Programs ·······································································
• Appendix A – Mathematics Program Alignments with Sample Course ··························· Appendices
• Appendix B – Faculty Data Sheets ····················································································
• Appendix C – Course Handbooks for Service Courses ······················································
• Appendix D – Survey Results ··························································································
• Appendix E – Students Meeting Graduation Requirements···········································
• Appendix F – NCATE Criteria and Results ·······································································
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PROGRAM REVIEW

FAIRMONT STATE UNIVERSITY

Program: Mathematics/Mathematics Education School: College of Science and Technology Date: 2 /12/

Program Catalog Description :

The mission of the mathematics degree programs is to equip students with analytic and problem solving skills for careers and graduate study. Classes develop student abilities and aptitudes to apply mathematical methods and ideas not only to problems in mathematics and related fields such as the sciences, computer science, actuarial science, or statistics, but also to virtually any area of inquiry. Students learn to communicate ideas effectively and to digest new information and concepts independently. Students are encouraged to develop intellectually and to become involved with professional organizations. Students interested in mathematics have the option of selecting one of the following degree programs:

the Bachelor of Science degree in Mathematics, as preparation for immediate employment or for graduate school.

the Bachelor of Arts in Education degree with a 5-Adult comprehensive specialization as preparation for teaching mathematics. Completion of a B.A. in Education with Specialization in Mathematics Grades 5-Adult results in concurrent completion of a B.S. in Mathematics. Students pursuing these degrees are advised in the math department. NOTE: MATH 1113, 1125, 1190, 3315, 3316, and 2212 are required for both degrees and should be completed early in the program.

the Mathematics 5-9 teaching specialization can be added to an Elementary Education degree or as a second specialization with a B.A. in Education.

It is expected that incoming students in this field will present a minimum of four units of high school mathematics, including two units of algebra, one unit of integrated geometry (or equivalent), and one advanced unit such as Trigonometry or Pre-Calculus. Students without this background may be required to complete appropriate lower-level courses in addition to the stated requirements. Students should consult with their advisor concerning credit for prerequisites and special examinations for course credit. All students majoring in mathematics must complete a minor. Students who are receiving a teaching certificate generally use Education as their minor.

Application/ Admission Requirements Students apply for admission to FSU through modern techniques by completion of an Application for Admission located on FSU’s homepage at www.fairmonstate.edu. Once the student fully completes the application process, the student’s application is reviewed for determination of admission.

Students seeking admission to Fairmont State University must be of the age of compulsory attendance in the state of West Virginia and file an application for admission. Applications and supporting credentials must be on file at least two weeks prior to the opening of a semester or term. All credentials submitted in support of an application for admission become the property of the University and will not be returned to the student. Any student admitted upon the basis of false credentials will be subject to immediate dismissal from the University.

Students who fail to register during the semester or term for which they have been admitted must file another application in order to gain admission at a later date. Separate applications for residence halls must be submitted to the Office of Residence Life. Any change in local address of any student at Fairmont State University must be reported to the Registrar.

The application for admission must specify the student’s desired degree or program objective. Admission to Fairmont State University does not guarantee admission to specific programs, which may be restricted due to limitations of staff, physical facilities, and space available for experiential training.

FAIRMONT STATE UNIVERSITY ADMISSION REQUIREMENTS FIRST-TIME FRESHMEN

1. Application for Admission
2. Official high school transcript or GED (sent by high school or Department of Education) (2.0 GPA or higher)
3. ACT or SAT Scores (18 ACT or 870 Composite SAT[combination of critical reading and math scores])
4. Transcript of home schooled students to include classes taken, credit hours and grades earned, graduation date and signature of home school provider.
5. Official College Transcript (if student has transfer credit)
6. Immunization Records (if born after January 1, 1957)

REQUIRED UNITS The Following Units Were Required: 4 English (including courses in grammar, composition, and literature) 3 Social Studies (including U.S. History) 4 Mathematics (three units must be Algebra 1 and higher) 3 Science (all courses to be college preparatory laboratory science, preferably including units from biology, chemistry and physics) 1 Arts 2 Foreign Language (Two units of the same foreign language)

Program courses

Enrollment

Five year course enrollment and success rate for all Mathematics program courses is provided below:

MATH

Course

Number 2008

-^2009 2009 -^2010 2010 -^2011 2011 -^2012 2012 -^2013 Total Enrollment over 5 Y

ears

Success Rate (^1113) 25 30 25 31 55 196 77. (^1125) NA NA NA 7 NA 7 57. (^1190) 70 77 84 75 88 394 70. (^2200) 20 30 25 29 34 138 65. (^2206) NA 9 NA 11 NA 20 75 (^2212) 9 14 20 15 10 68 76. (^2216) 25 22 27 27 31 132 83. (^3315) 24 33 36 32 33 158 86. (^3316) 18 10 16 10 16 70 84. (^3335) 16 9 18 8 11 62 72. (^3342) 8 NA NA NA NA 8 75 (^3361) 7 8 16 7 11 49 81. (^3362) 7 14 14 17 1 53 83 (^3372) 10 NA 15 NA 14 39 78. (^3375) 12 NA 8 NA 6 26 88. (^3391) NA 5 NA 14 NA 19 78. (^4400) 1 NA NA NA NA 1 100 (^4401) NA NA 8 NA NA 8 75 (^4431) 5 7 6 9 8 35 100 (^4498) 3 1 100

A list of course titles and descriptions are provided on the following pages.

MATH 2212 Sets, Relations and Functions 3 hrs. Topics to be studied are those related to sets, relations and functions which are common to most upper-level mathematics courses. PR: MATH 1170 or (MATH 1125 and MATH 1190). Fall semester only.

MATH 2216 Introduction to Discrete Mathematics 3 hrs. This course is designed to provide a survey of the reasoning and objects of study found in discrete mathematics. Topics considered include sets, relations, functions, combinatorics, graphs, trees, discrete probability and recurrence relations. Interspersed throughout the course will be material on the nature of proof and analysis of algorithms. PR: MATH 1115 or MATH 1170 or MATH 1185 or MATH 1190. Fall semester only.

MATH 3315 Calculus II 4 hrs. This course is a continuation of MATH 1190. Topics include applications of the definite integral, exponential and logarithmic functions, inverse trigonometric functions, techniques of integration, conic sections, plane curves and polar coordinates, limits involving indeterminate forms, improper integrals, sequences, and infinite series. Spring semester only. PR: MATH 1190.

MATH 3316 Calculus III 4 hrs. This course is a continuation of Math 3315. Sequences and series will be followed by a study of calculus of two and three variables. Topics include vectors, dot product, cross product, lines, planes, vector functions and their derivatives and integrals, the study of quadratic surfaces, partial differentiation, gradient and double and triple integrals. PR: MATH 3315 or (MATH 1186 and MATH 1190.) Fall Semester Only.

MATH 3335 Probability and Statistics 3 hrs. Course topics include sample spaces, events as subsets, probability axioms, finite sample spaces and equiprobable measure as special case, binomial coefficients and counting techniques applied to probability problems, conditional probability, independent events, Bayes’ formula, random variable, probability functions, density and distribution functions, special distributions, independent random variables, Poisson and normal approximation to the binomial and some statistical applications. Students will also learn estimation and sampling, point and interval estimates, hypothesis-testing, power of a test and regression. PR: MATH 1113, and MATH 3316 or concurrent enrollment in MATH 3316. Spring semester only.

MATH 3342 Numerical Analysis 3 hrs. In this course, students will investigate solutions of equations, functional iteration of equations, analysis of special methods such as the methods of false position and of Newton, iteration for systems of equations, reduction to first order systems, Gaussian elimination and some iterative methods for inversion. PR: COMP 1102 and CR: MATH 3316. Fall semester odd years only.

MATH 3361 Abstract Algebra 3 hrs. Writing Intensive Topics include sets, relations, functions, operations, algebraic systems such as integers, rationals and matrices, isomorphism and examples. Students will examine equivalence classes, groups, subgroups, cyclic groups, basic theorems, Lagrange’s theorem, homomorphism, normal subgroups, quotient group, the isomorphism theorems, rings, integers, matrices, polynomials, integral domains, fields and quotient field. The course will also cover ideals, residue class rings, unique factorization domains, Euclidean domains, integers, polynomials over a field, division algorithm, highest common factor and unique factorization in Euclidean domain. PR: ENGL 1108, MATH 1190 and MATH 2212. Spring semester only.

MATH 3362 Linear Algebra 3 hrs. This course covers vector spaces abstractly defined, linear dependence and independence, bases and subspaces, dimension of linear space, linear mappings, kernel and image of maps, rank of maps, linear maps as vector spaces, composition of mappings and multiplication of matrices, the relation between linear mappings and systems of linear equations, row reduced echelon matrix, invertible matrices, calculation of inverse, linear inequalities and half spaces. PR/CR: MATH 3315. Fall Semester only.

MATH 3372 Modern Geometry 3 hrs. A brief review of informal Euclidean geometry, including areas and volumes. The course will also include a formal development of Euclidean geometry, utilizing concepts such as incidence, convexity separation, distance functions and angular measurement functions. Other geometric topics such as topology, non-Euclidean geometry, finite geometries, projective geometry and transformational geometry are briefly introduced. PR: MATH 1125 and MATH 1190. Fall Semester. Even years only.

Success rates for Program Courses

*See note next page.

The success rate is based on the number of students passing the course with a letter grade of D or better. Each column depicts the number of students that passed and failed the major course per academic year. The last column provides the % success rate for each major course. Number of Students Passed or Failed/Withdrew Per Academic Year

2008 – 2009

2009 - 2010

2010 - 2011

2011 - 2012

2012 - 2013

MATH Course Passed Failed/Withdrew Passed Failed/Withdrew Passed Failed/Withdrew Passed Failed/Withdrew Pass

ed Failed/Withdrew 5 - year

P

ass

Rate (%)

**1113 *** (^) 21 4 23 7 19 6 24 7 41 13 77. (^1125) 4 3 57. **1190 *** (^) (^52 18 58 19 60 24 54 21 52 36) 70. **2200 *** (^) 12 8 22 8 17 8 16 13 23 11 65. (^2206) (^9 0 6 5 75). (^2212) 6 3 11 3 16 4 7 3 12 3 76. **2216 *** (^) 21 4 18 4 26 1 27 4 18 9 83. **3315 *** (^) (^21 3 32 1 31 5 27 6 25 7) 86. (^3316) 12 6 9 1 15 1 9 1 14 2 84. **3335 *** (^) 6 10 9 0 14 4 7 1 9 2 72. (^3342) 6 2 75. (^3361) 4 3 7 1 14 2 5 2 10 1 81. (^3362) (^5 2 10 4 12 2 16 1 1 0 83). (^3372) 8 2 13 2 12 2 78. (^3375) 10 2 7 1 6 0 88. (^3391) (^4 1 11 3) 78. (^4400) 1 0 100 (^4401) 6 2 75. (^4431) 5 0 7 0 6 0 9 0 8 0 100 (^4498) 3 0 1 0 100

Service courses Enrollment

Five year course enrollment for all Mathematics service courses is provided below:

MATH Course Number 2008

-^2009 2009 -^2010 2010 -^2011 2011 -^2012 2012 -^2013 Total Enrollment over 5 Years Success Rate (^1101) 209 173 201 224 176 983 60. (^1102) 87 76 61 98 85 407 85. (^1107) 509 565 579 494 507 2654 80. (^1112) 554 548 517 491 444 2554 66. (^1115) 119 115 142 147 137 660 67. (^1170) 28 15 NA NA NA 43 83. (^1185) 75 56 60 62 49 302 81. (^1186) 26 13 23 22 21 105 89. (^2251) 57 45 43 41 48 234 91. (^2252) 27 45 44 41 33 190 91. (^3353) 21 40 33 37 27 158 96.

A list of course titles and descriptions are provided on the following pages.

Service courses: The Mathematics program offers ten (10) service courses. A brief summary of each service course is provided below.

*Note : Math 1190, 2200, 2216, 3315, 3335 are used primarily for our majors but are also required by Computer Science. Math 1113, 1190 and 3315 can be used by multiple majors.

MATH 1101 Applied Technical Mathematics I 3 hrs. This course is an introduction to fundamental mechanics and techniques for performing operations with algebraic expressions, and subsequently solving linear equations, systems of linear equations and quadratic equations. The course also introduces trigonometric functions and is designed to develop methods of solving right angles and oblique triangles using trigonometry. PR: MATH ACT score of 19 or MATH SAT of 460 or COMPASS score of 36 or MATH 0095 or MATH 0088. Used by Tech majors

MATH 1170 Introduction to Mathematical Analysis 4 hrs. This course is designed to help those students pursuing a degree in mathematics (who have not had five years of high school mathematics) gain the experience required for courses at the calculus level and beyond. Topics include an introduction to formal logic and set theory, the principle of mathematical induction, properties of real and complex numbers with proofs, general functions and related notions, sequences and series. PR: MATH ACT score of 23, or MATH SAT 540 or Compass score of 63 or MATH 1115 No longer taught. Originally used by Computer Science.

MATH 1185 Applied Calculus I 4 hrs. This course is a study of calculus with an emphasis on its applications to science, business, technology and social science. Topics covered using the derivative consist of functions and their graphs, max/min problems, related rates, approximation of change and curvilinear motion. Topics covered using the integral consist of area, volume and accumulation functions. Graphing calculators and mathematical software will be introduced and used throughout the course. PR: MATH ACT score of 24, or MATH SAT 560 or COMPASS score of 67 or MATH 1115 or MATH 1102 with “B” or better. Used by Tech, Biology and Chemistry majors

MATH 1186 Applied Calculus II 4 hrs. A continuation of the study of calculus as applied to science, business, technology and social science. The integral will be further studied, including applications of area, volume, accumulation functions, curvilinear motion, solutions to some simple differential equations, and other applications chosen from a variety of disciplines. Students will examine sequences and series involving convergence and divergence, power series and Taylor polynomials and series. The calculus of vectors and multivariable functions will be introduced and partial derivatives and multiple integrals will be used to study applied problems from a variety of disciplines. Graphing calculators and mathematical software will be used throughout this course. PR: MATH 1185. Spring semester only Used by Tech, Biology and Chemistry majors

MATH 2251 Structure of the Real Numbers 3 hrs. This course starts with basic concepts of sets and continues with properties of operations and a logical development of the set of real numbers. Beginning number theory concepts and an introduction to probability are also included. This course connects structure to prior math knowledge and real-world applications. PR: Math 1112 or Math ACT of 23 or Math SAT of 540 or Compass score of 63, and admission to Teacher Education. Used by Elementary Education majors.

MATH 2252 Data Analysis and Geometry 3 hrs. This course offers an introduction to data analysis and statistics and the study of geometry. Included is descriptive statistics, standard and non-standard measurement, a formal and informal approach to geometry, van Hiele levels, and the use of dynamic geometry software. PR: Math 1112 or Math ACT of 23 or Math SAT of 540 or Compass score of 63, and admission to Teacher Education Used by Elementary Education majors.

MATH 3353 Math Methods for Elementary Teachers 3 hrs. This course is designed to prepare pre-service elementary school teachers to teach mathematics. Students will study tools for teaching mathematics, math teaching strategies, current topics in math education, problem solving and reasoning, and assessment. Numerous laboratory experiences are required such as tutoring, micro-teaching, and construction of a NCTM Standards-based unit. Used by Elementary Education majors.