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- Mathematics

### Mathematics

253.535.7400

www.plu.edu/math

math@plu.edu

The mathematics program at PLU is designed to serve five main objectives: (a) to provide backgrounds for other disciplines, (b) to provide a comprehensive pre-professional program for those directly entering the fields of teaching and applied mathematics, (c) to provide a nucleus of essential courses which will develop the breadth and maturity of mathematical thought for continued study of mathematics at the graduate level, (d) to develop the mental skills necessary for the creation, analysis, and critique of mathematical topics, and (e) to provide a view of mathematics as a part of humanisitic behavior.

**Beginning Classes**

Majors in mathematics, computer science and engineering, and other sciences usually take MATH 151 and MATH 152 (calculus). MATH 151 is also appropriate for any student whose high school mathematics preparation is strong. Those who have had calculus in high school may omit MATH 151 (see Advanced Placement section) and enroll in MATH 152 after consultation with a mathematics faculty member. Those who have less mathematics background may begin with MATH 140 before taking MATH 151. MATH 115 provides preparation for MATH 140.

Business majors may satisfy the requirement for the business degree by taking MATH 128, 151, or 152. (MATH 115 provides preparation for MATH 128.)

Elementary education majors may satisfy the requirement for the education degree by taking MATH 123 and MATH 124. (MATH 115 provides preparation for MATH 123.)

For students who plan to take only one mathematics course, a choice from MATH 105, 107, 123, 128, 140, or 151 is advised, depending on interest and preparation.

A placement test and background survey are used to help insure that students begin in mathematics courses that are appropriate to their preparation and abilities. Enrollment is not permitted in any of the beginning mathematics courses (MATH 105, 107, 115, 123, 124, 128, 140, 145, 151, and 152) until the placement test and its included background survey are completed. The link to the placement exam and survey is available at banweb.plu.edu.

The policy of the Mathematics Department regarding mathematics credit for students who have taken the AP Calculus exams (AB or BC) or the International Baccalaureate Higher Level Mathematics Exam (IBHL) is as follows:

*Consult with instructor if planning to take MATH 152.

If a student has taken calculus in high school and did not take an AP exam or IBHL exam, then the student may enroll in MATH 152 after consultation with a mathematics faculty member. In this case, no credit is given for MATH 151.

The Registrar’s Office determines whether a student meets the minimum entrance requirements by following the above rules. When a student has a deficiency, after taking the Math Placement Test, the student will receive a recommendation about how to remove the deficiency based on the test results.

If the test result shows that a student is qualified to take MATH 115 or a higher numbered math course at PLU, then the deficiency will be removed when the student successfully passes such a course. In addition, the student will receive Math Reasoning (MR) GenEd credit. Please be aware that credit taken from MATH 105, MATH 107, or any non-math course which carries the MR attribute does not remove a math deficiency.

If the Math Placement Test result shows that the student is not qualified to take MATH 115 or a higher numbered math course, the student will have to take a course at at community college to remove the deficiency in his or her minimum mathematics entrance requirement. The course content should be equivalent to a more difficult than high school algebra or geometry and it must be approved by the Mathematics Department.

**Mathematics and General Education Program Elements**

All mathematics courses will satisfy the mathematical reasoning (MR) element of the General Education Program. At least 4 semester hours are needed. All mathematics courses will satisfy the natural sciences, computer science, mathematics (NS) of the General Education Program. At least 4 semester hours are needed. A course cannot simultaneously satisfy mathematical reasoning (MR) and science and scientific method (SM) GenEd elements.

In fulfilling the Math Reasoning Requirement, students with documented disabilities will be given reasonable accommodations as determined by the Director of Disability Support Services and the appropriate faculty member in consultation with the student.

**Mathematics and the College of Arts and Sciences Requirement
**

*(see College of Arts and Sciences Requirements)*

All mathematics courses will satisfy the logic, mathematics, computer science or statistics part of Option III of the College of Arts and Sciences requirement. A course cannot simultaneously satisfy Option III of the College of Arts and Sciences requirement and a GenEd element.

**MATHEMATICS MAJOR REQUIREMENTS**

The foundation of the mathematics program for majors includes:

- MATH 151, 152, 253: The three-semester sequence of calculus
- MATH 331 (Linear Algebra)

Students with a calculus background in high school may receive advanced placement into the appropriate course in this sequence.

Students who have taken calculus in high school but do not have credit for MATH 151 do not need to take MATH 151 for the mathematics major or minor. However, they still need to complete the number of hours in mathematics as stated in the requirements.

Upper-division work includes courses in introduction to proof, linear algebra, abstract algebra, analysis, geometry, differential equations, numerical analysis, mathematical finance, and statistics. See the description of the courses and the major (either bachelor of arts or bachelor of science) for more detail. Students majoring in mathematics should discuss scheduling of these courses with their advisors. For example, MATH 499 extends over two semesters beginning with MATH 499A in the fall semester. May graduates begin this capstone course in the fall semester of the senior year, while December graduates must make special arrangements with the department chair by the start of the fall semester in the year preceding graduation.

A grade of C or higher is required in all prerequisite courses.

**Mathematics
**

*36 semester hours of mathematics, including 4 semester hours of supporting*

**Required:**MATH 151, 152, 242, 253, 317, 331, 433, 455, 499A, 499B**Required supporting:**CSCE 144**Strongly recommended is one course from the following:**CSCE 371; ECON 345: PHYS 153,163

**Mathematics
**

*44 semester hours of mathematics, including 8 or 9 semester hours of supporting*

**Required:**MATH 151, 152, 242, 253, 317, 331, 433, 455, 499A, 499B**8 semester hours from:**- MATH 321, 342, 348, 351*, 356, 381, 411, 480
- PHYS 354* (*Only one course from either MATH 351 or PHYS 354 may be used.)

**Required supporting**: CSCE 144 and one of the following: CSCE 348, 371; ECON 345; PHYS 153, 163

**Mathematics Education
**

*44 semester hours, including 4 to 5 semester hours of supporting*

**Required:**MATH 151, 152, 203, 253, 317, 321, 331, 433, 499A, 499B, and MATH/EDUC 446**One course from:**PHYS 125/135 Lab; PHYS 153/163 Lab; or CHEM 115**Strongly recommended:**MATH 455

All courses counted toward a mathematics education major must be completed with grades of C or higher in each course.

A minimum of 128 semester hours must be completed with a GPA of 2.50 or higher.

MATH/EDUC 446 must be completed with a B- or better.

**Note:** The B.S. degree with a major in mathematics education together with either a B.A.E. degree in secondary education or a master’s degree in education provides a path to teacher certification in secondary mathematics in Washington State. Passing the West-E exam in mathematics is required for teacher certification in secondary mathematics. Completion of the required math courses listed for the degree gives adequate preparation for the West-E exam.

**Financial Mathematics
**

*47 to 49 semester hours*

**Required:**

- Business: 8 semester hours
- Economics: 4 to 8 semester hours
*(not including ECON 101 and 102)* - Mathematics: 28 to 32 semester hours
*(not including capstone hours)* - Capstone: 2 to 4 semester hours
*(Directed Research or Internship)*

**Prerequisites:****Business:**BUSA 302 or permission of instructor for business courses**Economics:**ECON 101; ECON 102 or permission of instructor of ECON 345**Mathematics:**MATH 140 or placement into MATH 151 or higher

**Co-requisite strongly recommended:**PHIL 225: Business Ethics*(satisfies Philosophy GenEd element)***36 semester hours from the following:**- BUSA 335: Financial Investments (4)
- BUSA 437: Financial Analysis and Strategy (4)
- ECON 345: Math Topics in Economics (4)
- MATH 151: Calculus I (4)
- MATH 152: Calculus II (4)
- MATH 242: Introduction to Mathematical Statistics (4)
*(STAT 231 may be substituted with mathematics department permission)* - MATH 253: Multivariate Calculus (4)
- MATH 331: Linear Algebra (4)
- MATH 411: Mathematics of Risk (4)

**8 semester hours from the following:***(may only count either ECON 344 or MATH 348)*

Note: Within the groups of alternative courses listed below, highly recommended courses are marked by an **

- ECON 344: Econometrics (4)**
- MATH 342: Probability and Statistical Theory (4)**
- MATH 348: Applied Regression Analysis and ANOVA (4)
- MATH 351: Differential Equations (4)
- MATH 356: Numerical Analysis (4)
**4 semester hours from the following:**- BUSA 337: International Finance (4)
- BUSA 438: Empirical Finance (4)

**Capstone Experience:***(either MATH 495A or both MATH 499A and 499B)*- MATH 495A: Financial Mathematics Internship (2 to 4)
- MATH 499A: Capstone – Senior Seminar I (2)
- MATH 499B: Capstone – Senior Seminar II (2)

**MINORS**

**Actuarial Science
**

*A minimum of 24 semester hours, chosen from the following courses:*

- BUSA 302, 304, 335
- ECON 101, 301, 323, 344
- MATH 331, 342, 348, 356
**Also strongly recommended:**MATH 253**At least**12 semester hours must be taken from mathematics and at least 4 semester hours from economics

**Mathematics
**

*20 semester hours of mathematics courses, including:*

- MATH 151, 152, and 253; and 8 semester hours of upper-division mathematics courses, excluding MATH 446.

**Statistics
**

*A minimum of 16 semester hours to include:*

- CSCE 120 or 144
- STAT 231, 232, or 233; or MATH/STAT 242
**And at least:**8 additional semester hours of statistics selected from BUSA 467, ECON 344, PSYC 242, MATH/STAT 342, MATH/STAT 348. (Additional courses may be approved by the chair of the mathematics department.)See the Statistics section of this catalog for more details. Statistics courses taken for the statistics minor may not be simultaneously counted as elective credit for the bachelor of science major.The statistics minor is administered by the department of mathematics. For information, contact the chair of the department of mathematics.

**Courses Offered by Semester/Term:**

**Fall Semester:** 105, 115, 123, 124, 128, 140, 151, 152, 242, 253, 317, 331, 443, 446, 499A

**January Term:** 107, 203, 381**
Spring Semester:** 105, 115, 123, 124, 128, 140, 145, 151, 152, 245, 253, 317, 321, 331, 342, 348, 351, 356, 411, 455, 480, 499B

**Odd Years:** 203, 348, 480, 351; **Even Years:** 342, 356, 411

### Mathematics (MATH) Undergraduate-Level Courses

##### MATH 105: Mathematics of Personal Finance - MR, NS

Emphasizes financial transactions important to individuals and families: annuities, loans, insurance, interest, investment, time value of money. Prerequisite: PLU math entrance requirement. (4)

##### MATH 107: Mathematical Explorations - MR, NS

Mathematics and modern society. Emphasis on numerical and logical reasoning. Designed to increase awareness of applications of mathematics, to enhance enjoyment of and self-confidence in mathematics, and to sharpen critical thought in mathematics. Topics selected by the instructor. Prerequisite: PLU math entrance requirement. (4)

##### MATH 115: College Algebra and Trigonometry - MR, NS

A review of algebra emphasizing problem solving skills. The notion of function is introduced via examples from polynomial, rational, trigonometric, logarithmic and exponential functions. We also explore inverse trigonometric functions, identities, graphing and solution of triangle. Appropriate as preparation for Math 123, 128 and 140. Prerequisite: PLU math placement exam and two years of high school algebra. (4)

##### MATH 123: Modern Elementary Mathematics I: Number Sense and Algebraic Sense - MR, NS

Numeration systems and concepts underlying traditional computations. Field axioms, number theory, set theory. Patterns and variables, functions, proportionality, linear versus exponential growth. Emphasis on conceptual understanding of mathematics through problem solving, reasoning, and communication. Analyzing children's problem solving strategies. Intended for elementary teaching majors. Prerequisites: A qualifying score on the math placement test or a grade of C or higher in MATH 115. (4)

##### MATH 124: Modern Elementary Mathematics II: Measurement, Geometric Sense, Statistics and Probability - MR, NS

The units, systems and processes of measurement. Classification and measurement of geometric objects. Symmetry, transformations, congruence, dilations, similar figures. Display, analysis, and interpretation of data. Basic probability. Emphasis on conceptual understanding of mathematics through problem solving, reasoning, and communication. Analyzing children's problem solving strategies. Intended for elementary teaching majors. Prerequisite: A grade of C or higher in MATH 123. (4)

##### MATH 128: Linear Models and Calculus, An Introduction - MR, NS

Matrix theory, linear programming, and introduction to calculus. Concepts developed stressing applications, particularly to business. Prerequisites: Two years of high school algebra or MATH 115. Cannot be taken for credit if MATH 151 (or the equivalent) has been previously taken with a grade of C or higher. (4)

##### MATH 140: Analytic Geometry and Functions - MR, NS

Different types of functions, their properties and graphs, especially trigonometric functions. Algebraic skill, problem solving, and mathematical writing are emphasized. Prepares students for calculus. Prerequisites: MATH 115 or equivalent high school material. (4)

##### MATH 151: Introduction to Calculus - MR, NS

Functions, limits, derivatives and integrals with applications. Emphasis on derivatives. Prerequisite: Math analysis or pre-calculus in high school or MATH 140. (4)

##### MATH 152: Calculus II - MR, NS

Continuation of MATH 151. Techniques and applications of integrals, improper integrals, ordinary differential equations and power series, with applications. Prerequisite: MATH 151. (4)

##### MATH 203: History of Mathematics - NS

A study in the vast adventure of ideas that is mathematics from ancient cultures to the 20th Century. The evolution of the concepts of number, measurement, demonstration, and the various branches of mathematics in the contexts of the varied cultures in which they arose. Prerequisite: MATH 152 or consent of instructor. (4)

##### MATH 242: Introduction to Mathematical Statistics - NS

Data description, probability, discrete and continuous random variables, expectations, special distributions, statements of law of large numbers and central limit theorem, sampling distributions, theory of point estimators, confidence intervals, hypothesis tests, regression (time permitting). Cross-listed with STAT 242. Previously was MATH/STAT 341. Prerequisite: MATH 151. (4)

##### MATH 245: Discrete Structures - NS

Topics that are of relevance to computer scientists and computer engineers, including quantified logic, sets, relations, functions, recursion, combinatorics, and probability. Tools of logical reasoning, such as induction, proof by contradiction, and predicate calculus, will be taught and applied. Prerequisite: Math 152. (4)

##### MATH 253: Multivariable Calculus - NS

An introduction to vectors, partial derivatives, multiple integrals, and vector analysis. Prerequisite: MATH 152. (4)

##### MATH 287: Special Topics in Mathematics

To provide undergraduate students with new, one-time, and developing courses not yet available in the regular curriculum. The title will be listed on the student term-based record as ST: followed by the specific title designated by the academic unit. (1 to 4)

##### MATH 288: Special Topics in Mathematics

To provide undergraduate students with new, one-time, and developing courses not yet available in the regular curriculum. The title will be listed on the student term-based record as ST: followed by the specific title designated by the academic unit. (1 to 4)

##### MATH 289: Special Topics in Mathematics

To provide undergraduate students with new, one-time, and developing courses not yet available in the regular curriculum. The title will be listed on the student term-based record as ST: followed by the specific title designated by the academic unit. (1 to 4)

##### MATH 291: Directed Study

Supervised study of topics selected to meet the individual's needs or interests; primarily for students awarded advanced placement. Admission only by departmental invitation. (1 to 4)

##### MATH 317: Introduction to Proof in Mathematics

Introduces the logical methods of proof and abstraction in modern mathematics. Explores mathematical topics, including discrete mathematics, while familiarizing students with proof-related concepts such as mathematical grammar, logical equivalence, proof by contradiction, and proof by induction. Prerequisite: MATH 152. (4)

##### MATH 321: Geometry - NS

Foundations of geometry and basic theory in Euclidean, projective, and non-Euclidean geometry. Prerequisite: MATH 152 or consent of instructor. (4)

##### MATH 331: Linear Algebra - NS

Vectors and abstract vector spaces, matrices, inner product spaces, linear transformations. Proofs will be emphasized. Prerequisites: MATH 152 and one of MATH 245, 253, or 317. (4)

##### MATH 342: Probability and Statistical Theory

Continuation of MATH 242. Topics may include: joint and conditional distributions, correlation, functions of random variables, moment generating functions, inference in regression and one-way ANOVA, Bayesian and non-parametric inference, convergence of distributions. Cross-listed with STAT 342. Prerequisite: MATH 242. (4)

##### MATH 348: Applied Regression Analysis and ANOVA

Linear and multiple regression with inference and diagnostics; analysis of variance; experimental design with randomization and blocking. Substantial use of statistical software and emphasis on exploratory data analysis. Prerequisite: MATH 341 or consent of instructor. (4)

##### MATH 351: Differential Equations - NS

An introduction to differential equations emphasizing the applied aspect. First and second order differential equations, systems of differential equations, power series solutions, non-linear differential equations, numerical methods. Prerequisite: MATH 253. (4)

##### MATH 356: Numerical Analysis - NS

Numerical theory and application in the context of solutions of linear, nonlinear, and differential equations, matrix theory, interpolation, approximations, numerical differentiation and integration and Fourier transforms. Prerequisites: MATH 152 and CSCE 144. (4)

##### MATH 381: Seminar in Problem Solving

Designed to improve advanced problem solving skills for mathematical competitions, especially the Putnam Competition and the Mathematical Contest in Modeling. Pass/Fail only. May be taken more than once for credit. Prerequisite: Consent of instructor. (1)

##### MATH 387: Special Topics in Mathematics

##### MATH 388: Special Topics in Mathematics

##### MATH 389: Special Topics in Mathematics

##### MATH 411: Mathematics of Risk

This non-GenEd course introduces students to the mathematics underpinning financial investment in the presence of uncertainty. Students will investigate and employ probability models to assign values to individual financial instruments and to portfolios over short and long term time frames. Both analytic solutions and numerical solutions via software will be developed. Case studies will play a role in the course. Prerequisites: MATH 152, 341 and 342; ECON 101 or 301; BUSA 335; or consent of the instructor. (4)

##### MATH 433: Abstract Algebra

The algebra of axiomatically defined objects, such as groups, rings and fields with emphasis on theory and proof. Prerequisites: MATH 317, 331. (4)

##### MATH 446: Mathematics in the Secondary School

Methods and materials in secondary school math teaching. Basic mathematical concepts; principles of number operation, relation, proof, and problem solving in the context of arithmetic, algebra, and geometry. Cross-listed with EDUC 446. Prerequisite: MATH 253 or 331. (4)

##### MATH 455: Mathematical Analysis

Theoretical treatment of topics introduced in elementary calculus. Prerequisites: MATH 253, 317 and 331. (4)

##### MATH 480: Topics in Mathematics

Selected topics of current interest or from: combinatorics, complex analysis, differential geometry, dynamical systems chaos and fractals, graph theory, group representations, number theory, operations research, partial differential equations, topology, transform methods, abstract algebra, analysis. May be taken more than once for credit. Prerequisites vary depending on the topic. (1 to 4)

##### MATH 487: Special Topics in Mathematics

##### MATH 488: Special Topics in Mathematics

##### MATH 489: Special Topics in Mathematics

##### MATH 491: Independent Study

To provide individual undergraduate students with advanced study not available in the regular curriculum. The title will be listed on the student term-based record as IS: followed by the specific title designated by the student. Prerequisite: Consent of department chair. (1 to 4)

##### MATH 495A: Financial Mathematics Internship - SR

A research and writing project in conjunction with a student's approved off-campus activity. An oral presentation comparable in length with those required for MATH 499 is obligatory. Prerequisites: Senior (or second semester junior) financial mathematics major, and approval from the department prior to the commencement of the internship. (2 to 4)

##### MATH 499A: Capstone: Senior Seminar I - SR

Preparation for oral and written presentation of information learned in individual research under the direction of an assigned instructor. Discussion of methods for communicating mathematical knowledge. Selection of topic and initial research. With MATH 499B meets the senior seminar/project requirement. Prerequisite: Senior (or second semester junior) math major. (2)

##### MATH 499B: Capstone: Senior Seminar II - SR

Continuation of MATH 499A with emphasis on individual research and oral and written presentation. With MATH 499A meets the senior seminar/project requirement. Prerequisite: MATH 499A. (2)

Last Modified: February 24, 2015 at 10:15 pm