MATH 105 – Mathematics of Personal Finance

This course focuses on strengthening mathematics concepts and quantitative skills essential for managing one’s personal finances.  Students will explore topics such as budgets, investments, loans, credit cards, savings, retirement, insurance, taxes, depreciation and the time value of money.  The topics covered in this course are of a practical nature and can be applied to your daily life!  The course is designed to build self-confidence in one’s algebra skills and learn where you can apply those skills when planning for your financial future.

Prerequisite: Placement into this course through the PLU math placement system.

MATH 107 – Mathematical Explorations

This course explores the uses of mathematics in contemporary society. The themes and content of the course are selected by the instructor, and may vary from semester to semester.  Nonetheless, this course always has an emphasis on logical and numerical reasoning.  The emphasis on quantitative literacy usually includes ratios, percents, and basic statistics, as well as financial literacy, including compound interest.  Some past themes have included cryptography, voting methods, marketing, mathematics of money, and probability and statistics.  The course is designed to increase awareness in the many ways that mathematics is used in everyday life, as well as to enhance the students’ enjoyment of and self-confidence in math, and to sharpen students’ critical thinking.

Prerequisite: Placement into this course through the PLU math placement system.

MATH 115 – College Algebra and Trigonometry

This course is a review of algebra and trigonometry, emphasizing problem-solving skills.  The main purpose of this course is to introduce students to many of the elementary functions important in common applications of mathematics.  These functions include polynomial functions, rational functions, exponential functions and logarithmic functions.  We will use plots of these functions in the coordinate plane, combining algebra and geometry, to develop visual cues to help understand these functions.  In addition, we will introduce the trigonometric functions, both in the context of ratios of sides of right triangles and via plots in the plane.

This course provides preparation for Math 123, Math 128 and Math 140.

Prerequisites: Placement into this course through the PLU math placement test.

MATH 123 – Mathematics for Elementary Education I

This course is intended for preservice K-8 teachers.  Elementary teachers need a strong conceptual understanding of mathematics to successfully teach children mathematics. This course gives future elementary teachers an opportunity to explore elementary school mathematics in depth, through hands-on learning and with consideration of children’s mathematical thinking strategies.  This class focuses on two of the five recognized strands of school mathematics: number sense and algebraic sense.  Students in this course will:

• Extend and generalize geometric and number patterns;
• Understand place value;
• Understand the common algorithms used for operations on whole numbers, integers and rational numbers;
• Understand fractions, percentages, and ratios.

Special emphasis is placed on the Standards for Mathematical Practice (part of the Common Core State Standards for Mathematics), especially: persevering in solving problems, constructing viable arguments, and critiquing the reasoning of others.  In particular, students will learn to explain Why rather than just explaining How, and they will continually justify their reasoning to the instructor and their peers, thus developing the ability to explain mathematical concepts to their future students.

Prerequisites: The completion of Math 115 with a grade of C or better, or math placement into a more advanced math course than Math 115.

MATH 124 – Math for Elementary Education II

This course, as a continuation of MATH 123, is intended for preservice K-8 teachers.  Its focus is on enhancing the students’ conceptual understanding of the remaining three recognized strands of school mathematics: geometry, measurement, and probability and statistics.  As in MATH 123, students will engage in hands-on learning, and consider children’s strategies.  Students will discuss topics such as:

• Properties of polyhedra;
• Classification of triangles and quadrilaterals;
• Properties of transformations;
• Discovering area formulas for special quadrilaterals as well as surface area and volume formulas for special three-dimensional solids;
• Statistical analysis of data including appropriate graphical representations of data
• Basic probability formulas.

Special emphasis is placed on the Standards for Mathematical Practice (part of the Common Core State Standards for Mathematics), especially: persevering in solving problems, constructing viable arguments, and critiquing the reasoning of others.  In particular, students will learn to explain Why rather than just explaining How, and they will continually justify their reasoning to the instructor and their peers, thus developing the ability to explain mathematical concepts to their future students.

Prerequisite: Completion of Math 123 with a grade of C or better.

MATH 128 – Linear Models

This is the required mathematics course for business majors, and as such, most of the applications in the course are taken from business, broadly interpreted.  The course typically covers several distinct subjects:

Systems of linear equations – formulation and solution;

Systems of linear inequalities in two variables and applied optimization;

An introduction to matrices and vectors;

Logarithms and Exponentials;

Basic Time Value of Money;

Applied differential calculus of a single variable.

Since this course is not intended for mathematics majors, there is a strong focus on techniques and applications, and only a minimal focus on theoretical justifications.  Consequently, this course cannot substitute for Math 151, the first calculus course intended for students majoring in mathematics, economics and the physical sciences.  Students who intend to emphasize the finance or economics aspects of business are strongly encouraged to take Math 151 rather than Math 128.

Prerequisites: The completion of Math 115 with a grade of C or better, or math placement into Math 128.  This course cannot be taken for credit if you have already passed Math 151 (or equivalent) with a grade of C or better.

MATH 140 — Precalculus

This is, essentially, boot camp to prepare you for calculus! In this course, you will solidify your understanding of various functions that play important roles in calculus and other areas of higher mathematics. You will study properties of functions (such as their domains and ranges), combinations of functions (including composition of functions and transformations of graphs), and inverse functions (which only sometimes exist!).  You’ll also learn about elementary functions (such as polynomial, power, exponential, logarithmic, trigonometric, and inverse trigonometric functions), and how to use these functions in applications (such as population growth or radioactive decay). Finally, you’ll explore trigonometric identities in some detail, and learn about the polar coordinate system (an alternate way of representing points in the plane whose use simplifies many computations in applied mathematics).

Prerequisites: The completion of Math 115 with a grade of C or better, or math placement into Math 140.

MATH 145 – Introduction to Biostatistics

This course introduces students to the basic ideas and practices of statistics in the context of biology and the health sciences.  Rather than using mathematics to develop the techniques of statistics, this course focuses on the development of statistical thinking.  In particular, students discover how natural variability, an inherent reality of biological systems, complicates our ability to model and measure “typical” values for species or outcomes of an experiment.  Students will learn how to use data-driven models and randomness to start to make sense of measurements and experimental results, and to understand how much certainty we can (and cannot) extract from naturally noisy data.  Topics covered include:

Descriptive statistics – data summaries such as means and standard deviations;

Data display – histograms, dot plots, regression plots, q-q plots;

Fundamental probability models: uniform, binomial and normal distributions;

Confidence intervals – how to use data to make estimates about populations;

Hypothesis tests – how strongly does data agree with models and visa versa;

Biostatistics is an entire major in its own right; rather than attempting to provide a cookbook introduction to all of the statistical techniques and tests that a biologist might need, this course is intended to help students understand the principal threads of statistical thinking.  As students encounter more advanced statistical techniques throughout their education, they should be able to anchor those techniques to ideas learned in this course.

Students will typically learn to use MINITAB software to analyze small data sets.

Prerequisites: The completion of Math 140 with a grade of C or better, or math placement into Math 151 or a more advanced course.

MATH 151 — Calculus I

Slope tells something about the rate of change in a line.  This is an extremely useful concept, but has the shortcoming of only being applicable to lines.  In Calculus I, this difficulty is overcome by developing a generalization known as the derivative, essentially a concept of slope that can be applied to functions other than lines.  Armed with the derivative, we can answer questions about the rate of change of functions, allowing us to find maxima or minima of functions, study velocity and acceleration of physical bodies, understand chemical reaction rates, and model population growth. We can graph complicated curves, and describe the relative efficiency of rival computer algorithms. Indeed, the calculus provides a universal language to precisely describe and compute rates of growth and decrease.

Prerequisites: The completion of Math 140 with a grade of C or better, or math placement into Math 151.

MATH 152—Calculus II

Nearly everyone knows that the area of a circle is , but few think about how this and similar formulas arise.  In Calculus II, we use the concept of the integral to study the area under curves.  This naturally generalizes to the study of volumes of solids in space.  Amazingly, this same concept, combined with the derivative (from Calculus I) can be used in many unexpected and powerful ways.  Quantities as diverse as the GNP (gross national product) in economics and the total run time of a computer program can be described as an area under an appropriate curve.  Calculus II provides tools to compute these quantities and to relate them to the functions that describe their rates of change.

It is possible for infinitely many numbers to sum to a finite value!  For example, it can be shown that .  The integral and derivative are used as tools to help us understand such infinite series.  In turn, these series help us to better understand many well-known and lesser-known functions.  For example,  and can be written as infinitely long “polynomials”, and can be approximated reasonably well by certain special polynomials of degree four or five.

Prerequisites: The completion of Math 151 with a grade of C or better, or math placement into Math 152.

Math 203—History of Mathematics

Often, when we learn mathematics, we learn it without the story of who developed it, when it was developed, and why.  In the History of Mathematics, we look at the stories behind the mathematics.  These stories take us around the earth and through millennia in time.  We begin about 4000 years ago with the ancient civilizations of Egypt and Mesopotamia, where considerable mathematics was already known, particularly algebra and the art of computation.  We also explore the early mathematical discoveries of China and India.  Next, we explore the amazing flowering of mathematics that occurred in ancient Greece: geometry, astronomy, trigonometry and much more.  Then we investigate further developments of algebra by the Arabic mathematicians of medieval times; in fact, our word, algebra, is from the Arabic.  We next move to Europe to see algebra in Italy, analytic geometry in France, logarithms in Scotland, and the beginnings of calculus almost everywhere.  We follow the development of calculus, and see how it changed from the early 1600’s to the early 1800’s.  We then look at the surprising story of non-Euclidean geometry, which was developed in the 1800’s.  Our survey of more recent discoveries will be brief, restricted by their technical difficulty and their amazing abundance.

We will study the biographies of a number of mathematicians, and look at the special difficulties experienced by women mathematicians.

Since many of the students in this class intend to become mathematics teachers, we will examine the histories of specific areas of mathematics commonly taught in the schools, such as number systems, algebra, geometry and trigonometry.

Prerequisites: The completion of Math 152 with a grade of C or better, AP or transfer credit for Math 152, or consent of the instructor.

MATH/STAT 242—Introduction to Mathematical Statistics

As the title suggests, we will apply mathematical techniques to develop some of the fundamental ideas of statistics.  So just what is statistics?  Statistics is the art of extracting patterns from data.  This might consist of summarizing complicated data, whether numerically, graphically or by constructing a simple mathematical model that connects pieces of data to one another.  Whereas mathematics uses a language of certainty, theorems and proofs, statistics has developed precisely to deal with uncertainty, estimates, bounds and probabilities.

In this course we will examine answers to several important questions in statistics.  How do you describe a data set so as to capture its ‘center’ and its variation?  This will lead to topics such as the mean and the variance of a sample.  What is probability and how do we model it mathematically?  This will lead to the classical distributions: binomial, Poisson, exponential and normal.  How do you decide whether your preconceptions about a large population are in agreement with the data obtained from a sample? This will lead us to confidence intervals and hypothesis testing.

Throughout the course we will see that statistics is much more that just the application of mathematical techniques.  We will see that, before we can apply the mathematics, we must have good data and reasonable models.  After we have done our mathematical analysis, we must still decide whether we have enough certainty to make conclusions.  In short, we will be the lawyers, judge and jury in the court of data analysis.

We will apply the techniques of algebra and calculus to investigate probability, to develop models and to explore their properties and understand why some estimation techniques have better properties than others do.  We will apply Minitab statistical software to real world data sets and to simulated data sets.

This course is cross-listed under both mathematics and statistics.  Students can take this course for the mathematics major and minor, the statistics minor and the actuarial science minor.

Prerequisites: The completion of Math 151 with a grade of C or better, or math placement into Math 152 or a more advanced course.

MATH 245—Discrete Structures

The possession of logical reasoning skills is essential for anyone interested in computer science.  In this class, students enhance these skills by studying a variety of mathematical topics related to the study of computer science, which may include propositional logic, set theory, relations, functions, combinatorics, and graph theory, as well as applications of these topics.  Students also learn proof-techniques such as induction (a “domino” technique that allows one to prove that a statement relating to a variable n is true for all positive integers n) and proof by contradiction (in which one proves a desired result by showing that if it isn’t true, nonsensical things happen).  This increases students’ mathematical maturity and their ability to make reasoned arguments, both prerequisites for successful programming.  Topics vary from term to term, and may depend on student interest.  Here is a sample of things students might learn in this class:

(1)  The logical difference between the statements, Not all people have red hair, and All people do not have red hair;

(2)  How to show that 1+2+3+…+n= n(n+1)/2, for any positive integer n;

(3) How to use induction to prove the correctness of a loop in a computer algorithm.

(4)  How to show that the set of integers and the set of rational numbers have the same “size”, but the set of real numbers is “bigger”;

(5)  How to compute the probability of getting a royal flush in poker.

The course is intended primarily for computer science majors and math majors.

Note: Although this class has Math 152 as a prerequisite, to ensure the mathematical preparedness of its students, most of the material in this course is not directly related to that learned in the calculus sequence.

Prerequisites: The completion of Math 152 with a grade of C or better, AP or transfer credit for Math 152, or math placement into Math 253 or a more advanced course.

MATH 253—Calculus III

Most things are related to more than just one input factor.  For example, your minimum monthly credit card payment depends on the total you owe and your interest rate.  The amount you actually pay depends on the minimum payment due and the amount you have available to pay.  The growth rate of a deer population depends on the size of the population, its age distribution, the food supply and the frequency of predation. The pressure exerted by gas in a cylinder depends on the amount of gas, its temperature and the volume of the cylinder.

Other functions may only depend on one variable, but give an output that is more than just one number.  For example, a person traveling around the world has, at any given time, a latitude and a longitude (and perhaps an altitude too if s/he is in an airplane).  Thus, position can be considered a function of time but it cannot be represented by a single value; it must be given as a doublet (or triplet) of numbers representing latitude and longitude (and altitude).  Such a doublet or triplet can be represented as a vector.

Calculus III extends the ideas of Calculus I and II by considering derivatives and integrals of functions with more than one variable, and of vector-valued functions. Along the way, noncartesian coordinate systems (such as polar coordinates) are discussed.

Prerequisites: The completion of Math 152 with a grade of C or better, AP or transfer credit for Math 152, or math placement into Math 253.

MATH 317—Introduction to Proof in Mathematics

In mathematics, we accept a statement as true only if we have a proof that it is true.  Since the method of proof is so basic to mathematics, anyone who seriously wants to learn mathematics beyond a fairly elementary level must be able to understand proofs and be reasonably proficient at constructing them.  The purpose of this class is to teach you to understand proofs and to develop your skills at constructing proofs.  Skill at proving develops over a long period of time; this class is only a beginning. The best way to learn to do proofs is to do them, so you will be given plenty of opportunity to practice proving results.

We will begin with an introduction to logic.  Logic is a tool that we will use to analyze proofs to see if they are correct as well as to help us to construct proofs. We will practice writing proofs in a number of areas of mathematics: set theory, including infinite sets, inequalities and functions.  We will study the whole numbers using mathematical induction.  In addition to the usual lecture format, a good deal of class time will be spent with students presenting their proofs to the class or constructing proofs together.

This class is good preparation for Linear Algebra (MATH 331), Abstract Algebra (MATH 433), Analysis (MATH 455), and other advanced mathematics classes.

Prerequisites: The completion of Math 152 with a grade of C or better, AP or transfer credit for Math 152, math placement into Math 253 or a more advanced course, or consent of the instructor.

MATH 321—Geometry

The geometry most of us learned in high school is based on Euclid’s famous 5 Postulates and works well for describing things in or on a flat surface. However, the surface of our world is not flat, and any pilot or ship’s navigator must understand the rules of spherical geometry.

The discovery of two-dimensional non-Euclidean geometries early in the nineteenth century by Gauss, Bolyai and Lobachevski allowed us to ask for the first time, “Could the geometry of the three-dimensional universe in which we live also be non-Euclidean?” The work of Riemann and, later, Minkowski provide a geometric structure for Einstein’s theory of relativity and for modern theories of cosmology where the ultimate collapse or expansion of the universe is related to the curvature of space itself.

The discovery of two-dimensional non-Euclidean geometries also initiated a momentous shift in our view of the entire mathematical enterprise.  The question of axiomatic foundations raised by the non-Euclidean geometries now pervades all branches of the subject and forms the acid test of mathematical validity.

This class examines the foundations of geometry that lead to Euclid’s geometry in the plane and to other possible geometries, most notably spherical and hyperbolic, and concentrates on exploring the rules of geometric logic that are universal.

Prerequisites: The completion of Math 152 with a grade of C or better, AP or transfer credit for Math 152, math placement into Math 253151 or a more advanced course, or consent of the instructor.

MATH 331—Linear Algebra

Why algebra?  Algebra was invented because of the limitations of our geometric intuition.  In applications ranging from business to engineering to the social sciences, it is often useful to work with data that naturally correspond to points in the plane, or in three-dimensional space, or even in fifty-dimensional space.  Certainly, we could draw pictures or build models to avoid algebra for points in the plane or in three-dimensional space, but what pictures or models could help us to “see” in fifty dimensions?  This obstacle motivates the development of vectors and the development of algebraic rules and techniques for manipulating them.  In this course we pursue two intimately related subjects: matrix theory and linear algebra.

Matrix theory is concerned with vectors and matrices.  Vectors are the n-dimensional generalizations of the ordered pairs representing points in the plane.  We will investigate how our geometric concepts naturally imbed in algebraic concepts.  We will learn how the geometry of lines and planes, lengths and angles is replaced by systems of equations and operations on vectors.  Further, we will see how systems of equations can be analyzed in terms of the properties of a single algebraic object: the matrix.

Linear algebra is the study of sets of vectors and how operations on individual vectors can be applied to entire sets.  Linear algebra is the abstraction of the fundamental properties displayed by vectors and matrices.  This abstraction allows us to use the knowledge and skills developed working with vectors and matrices to answer questions about the behavior of wave functions in quantum mechanics, signals in Fourier analysis, and the nature of solutions to important families of differential equations.

This course is very different from calculus.  In calculus, there are relatively fewer theoretical ideas, and most of the course is devoted to applying those ideas and the associated techniques to specific computations.  In MATH 331, students learn a large variety of new ideas and, while calculations are important, they are primarily tools for understanding the examples that motivate the theory.  Consequently much of the work in this course is focused on explaining why certain relationships between ideas are true or why certain sets have specified properties, rather than on simply producing a slope or an integral or a number.  Calculus is a prerequisite for this course primarily because students rarely have adequate facility with mathematical thinking, working with equations, working extensively with symbols, thinking about exceptions or using technical language—prior to completing the calculus sequence.

Prerequisites: The completion of Math 152 and one of Math 245, 253 and 317, both with a grade of C or better.

MATH/STAT 342—Probability and Statistical Theory

This is a continuation of MATH/STAT 242 (Introduction to Mathematical Statistics).  In this class, students will expand their basic knowledge from 341 into broader and deeper probability and statistics theory.  For instance, students will learn about conditional distributions of multiple random variables, limiting distributions, moment generating functions and higher moments than the mean and variance. Students will learn more methods for testing statistical hypotheses, such as the two-sample T test, the F-test and non-parametric methods.

To insure that students learn more than just theoretical ideas a term project applying class knowledge to solving real world problems is usually assigned.  Minitab will be used for the data analysis.

Students are required to complete STAT 231 or MATH/STAT 242 with a grade of C or better prior to enrolling in this class, or have consent of the instructor.  MATH/STAT 342 is cross-listed under mathematics and statistics.  Students can take this course for the mathematics major (or minor), the statistics minor and the actuarial science minor.

MATH/STAT 348—Applied Regression Analysis and ANOVA

Regression analysis of data is a powerful statistical tool that is widely used in biology, psychology, management, engineering, medical research, government and many other fields.  It provides a technique for building a reasonable mathematical model that relates the mean value of a response (e.g., profit) to various independent variables or predictors (e.g., advertising budgets, size of inventory, etc.).

Any prediction or estimation based on a random sample of data will contain a unknown error component.  In this course, students will learn various methods to build a best regression model for a given set of data under constraints so that the error component is minimized.

When the relation between the output variable and the independent input variables is linear, we call the model linear regression.  Students will also learn about nonlinear regression, where there can be a nonlinear relationship (such as quadratic or exponential) between the output and the inputs.  Real world problem-solving skills are emphasized.  Minitab is used extensively for the data exploration and data analysis.  A term project (with open topics) is normally assigned for students to explore knowledge beyond the classroom.

Students are required to complete STAT 231 or MATH/STAT 242 with a grade of C or better prior to enrolling in this class, or have consent of the instructor.  MATH/STAT 348 is cross-listed under mathematics and statistics.  Students can take it for the mathematics major (or minor), the statistics minor and the actuarial science minor.

MATH 351—Differential Equations

Differential equations are a powerful tool in constructing mathematical models for the physical world.  Their use in industry and engineering is so widespread and they perform so well that they are among the most successful of modeling tools.

For example, a cup of hot coffee is initially at and is left in a room with an ambient temperature of .  Suppose that initially it is cooling at a rate of  per minute.  Then the model for the cup’s temperature is .  This is an example of a differential equation.  We are interested in predicting the temperature, T, of the coffee at any time t.  We can also ask, “How long does it take the coffee to cool to a temperature of, say,

Prerequisite: Completion of Math 253 with a grade of C or better, or have consent of the instructor.

MATH 356—Numerical Analysis

When one pushes the square root button on a calculator to compute the square root of 2, one should ask, “How does the calculator do it?”  Numerical analysis deals with implementing numerical methods to answer questions like this one.

While numerical methods have always been useful, since the invention of computers, the role of numerical methods in scientific research has become essential.  No modern applied mathematician, physical scientist or engineer can be properly trained without some understanding of numerical methods.  There is more involved here than just knowing how to use the methods.  One needs to know how to analyze their accuracy and efficiency.  Numerical analysis is a broad and challenging mathematical activity, whose central theme is the effective constructability of various kinds of approximations.

Prerequisites: Completion of Math 152 with a grade of C or better, and completion of CSCE 144 with a passing grade; or consent of the instructor.

MATH 381 – Seminar in Problem Solving

This 1 credit course is usually offered during J-term as an independent study course, and it is preparatory for participation in the international Mathematical Competition in Modeling, a multiday, small team competition based on solving an open-ended question in applied mathematics that is held early in February each year. Students may repeat this course more than once for credit.  This course can also be taken as an independent study course in preparation for the Putnam Exam, which is held in early December each year.

Prerequisites: Consent of the instructor.

MATH 411 – Mathematics of Risk

This course introduces students to the fundamental mathematical ideas that underpin finance, with an emphasis on the time value of money and the concept of no-arbitrage pricing.  You will study both deterministic financial models and probabilistic financial models.  In deterministic models such as deposit accounts and loans with fixed interest rates, as well as corporate and government bonds, all parameters that determine the value of an investment are known at all points in time.  In probabilistic models, such as floating rate bonds or the Black-Scholes option pricing model, prices depend on future quantities that are uncertain but which have known probability distributions.

This course is self-contained with respect to knowing about financial instruments and financial pricing models.  While students should know the basics of probability as covered in Math 242, more advanced probability content (such as that covered in Math 342) will be covered as needed.  The most important prerequisites are comfort with working with multivariate functions and their algebraic and calculus properties, and an interest in economics and finance.  This course is an excellent preparation for careers in actuarial science, finance and economics.

Prerequisites: In addition to the completion of Math 152 and either Stat 231 or Math/Stat 242, both with grades of at least C, student must have consent of the instructor.

MATH 433—Abstract Algebra

If you can tell time, you already know some abstract algebra: you just don’t know you know it!  Suppose you have lunch every day at 1:00pm.  Then you’ll have lunch at 1:00pm today and at 1:00pm tomorrow.  We just called both of those times ‘1:00pm’, but they’re not really the same moment in time, since they’re occurring on different days!  It turns out they both can be thought of as representatives of a coset of 24Z in R; this coset, in turn, is an element of the factor group R/24Z.

Huh, you ask?  What’s a coset?  What’s Z?  What’s R?  What’s a factor group?!  Take this class and find out!  Abstract algebra is the study of algebraic structures such as groups, rings and fields.  (You don’t know what these objects are yet, but if you take this class you will!)  You encounter such objects everywhere in math: the coordinate plane is an example of a group; the set of all  matrices over the real numbers is an example of a ring; the set of all real numbers is a field.  By studying these structures abstractly, we can give one proof for many results that hold for wildly different objects, instead of proving each result for each object separately.

Abstract algebra is a beautiful and powerful area of mathematics and it is an essential part of any mathematics curriculum.  It has applications in many sciences, from physics to chemistry, in addition to having extremely important uses in areas such as cryptography.

While the concepts in this class require minimal prerequisite knowledge of topics such as calculus, this class is heavily proof-based and requires a large amount of mathematical maturity.  The ability to write grammatically and to make logical arguments is extremely important, while the ability to differentiate will be of little, if any, use.  Conceptual understanding, not a calculator, is at the heart of this course!

Prerequisites: The completion of Math 317 and Math 331, both with grades of C or better.

MATH/EDUC 446—Mathematics in the Secondary School

This course has been designed for prospective teachers of middle school and high school mathematics and it reflects the recommendations of the National Council of Teachers of Mathematics (NCTM).  The following excerpt is from the NCTM Principles and Standards book:

The Teaching Principle

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

Teachers need to know and use ‘mathematics for teaching’ that combines mathematical knowledge and pedagogical knowledge. They must be information providers, planners, consultants and explorers of uncharted mathematical territory. They must adjust their practices and extend their knowledge to reflect changing curricula and technologies and to incorporate new knowledge about how students learn mathematics. They also must be able to describe and explain why they are aiming for particular goals.

The course takes the art of teaching through a series of motivational ideas suitable for many grade levels and abilities and includes a discussion of activities, materials and manipulatives suitable for classroom use. Problem solving and heuristics is a major theme in the course. Other topics covered include cooperative learning, questioning techniques, technology, lesson planning, homework options, mini-discovery lessons and technology lessons.

In this course, preservice teachers will:

• Acquire tools necessary for effective mathematics teaching, e.g. lesson and unit planning, motivation and questioning techniques, cooperative learning, assessment, manipulatives, technology, enrichment;
• Engage with mathematics activities suitable for 6-12 grade mathematics classrooms;
• Engage with the Common Core State Standards in Mathematics, currently in place in Washington and 41 other states;
• Become informed about the history of and current issues in mathematics education, e.g. achievement gap, national and state standards, teaching English Language Learners, standardized testing, and culturally responsive teaching;
• Spend 20 hours in a secondary mathematics classroom, observing and assisting the teacher.

This course is cross-listed with EDUC 446.

Prerequisites: The completion of either MATH 253 or Math 331 with a grade of C or better.

MATH 455—Mathematical Analysis

Why does calculus work?  In this course, we examine the foundations of calculus.  What properties of the real numbers distinguish them from the rational numbers?  What role do these differences play in the development of such fundamental concepts as limits and convergence?  What does continuity really mean, and why do we need it?  Along the way, we will study sequences, series and limits, first of numbers, and then of functions.  One consequence of our study will be a better appreciation of the central role of power series in many of the results of calculus.

This course is strongly recommended for anyone considering a graduate degree in pure or applied mathematics, statistics, theoretical physics or operations research.  Surprisingly, a deep understanding of the theoretical underpinnings of calculus is necessary to make progress in such applied areas as optimization, numerical analysis, financial modeling, probability and differential equations.

This course is almost entirely focused on formal definitions and rigorous proofs.  Students are encouraged to have as much exposure to proofs as possible prior to enrolling in this course.

Prerequisites: The completion of Math 253, Math 317 and Math 331, all with grades of C or better.

MATH 495A – Financial Internship Capstone

This capstone option is only available to financial mathematics majors who are participating in an internship with a financial or actuarial organization.  Math 495A can be taken as soon as the internship has been completed, and is usually taken in the first regular academic semester following the internship.  As with the regular capstone, Math 499A&B, each student completes a research project culminating in a written paper and an oral presentation to students and faculty.  Prior to selecting this option, you must have permission of the professor supervising the financial mathematics degree.  Approval must be granted prior to the start of the internship.

MATH 499A & B—Capstone: Senior Seminars I & II

Just as an architectural capstone tops a building, your capstone project is the crowning element in your undergraduate studies of mathematics.  In this sequence of classes, you choose a mathematical topic that interests you, and explore it on your own, with the help of a faculty advisor.  You can choose to learn a topic that is new to you, or look in greater depth at something you had already begun to learn. You are not expected to do original research for your mathematics capstone; rather, you are expected to demonstrate a facility for independently learning mathematics; your mastery of the mathematical content you have chosen to learn; an understanding of the role definitions and proofs play in mathematics; and skill in the written and oral communication of mathematics.

In MATH 499A, you will choose a topic and advisor, with the help of your instructor, as well as attend mathematics seminars, to see what oral presentation of mathematics looks like.  Your instructor may also provide further instruction that will help you in your work, such as LaTeX or library research tutorials.  In January and during MATH 499B, you will work on your project, learning and assimilating the mathematics you’ve chosen to study.  Finally, near the end of the spring term, you will present your work both in a paper and in a mathematical talk, as well as attend the talks of your capstone peers.

This course is normally taken during the student’s last two semesters at PLU.

Prerequisites: Consent of the instructor.

Last updated: November 12, 2015