Mathematics

How do you solve for the unknown?

How do you represent a real-world situation with an equation and a graph?

This foundational course focuses on the skills that students will need to be successful in all future math course. Students will explore writing and solving linear equations, powers and exponents, quadratic equations, polynomials and factoring, graphing and solving linear inequalities, and functions. Throughout the course, the mathematical concepts will be taught with an emphasis on real-world applications and technology. By the end of the this course, students will be prepared for Geometry.

How can you solve, graph, and formulate mathematical functions? What are the advantages and limitations when using mathematical functions to model real-life situations?

This course reviews and builds on topics presented in Algebra I and goes on to the study of linear programming and imaginary numbers. Students explore the behavior and applications of polynomial, exponential, logarithmic, and trigonometric functions.

How can you solve, graph, and formulate mathematical functions?
What are the advantages and limitations when using mathematical functions to model real-life situations?

This course reviews and builds on topics presented in Algebra I and goes on to the study of linear programming and imaginary numbers. Students explore the behavior and applications of polynomial, exponential, logarithmic, and trigonometric functions. Advanced level mathematics classes spend less time reviewing foundational material and investigate many topics at a greater depth than standard classes. Math department approval is required.

Linear algebra is an area of mathematics devoted to the study of structure-preserving operators on special sets (linear operators on vector spaces). Linear algebra is a cornerstone of any mathematics curriculum for two important (and related) reasons:

1. The theory of linear algebra is well understood and so when mathematicians encounter a challenging problem in other fields, they often equate it to one in linear algebra.
2. The spaces and operations studied in the subject are commonplace in many different areas of mathematics, science, and engineering.

Over the year we will study many topics that form a central part of the language of modern science. The successful student will be able to (amongst other things):

• Compute with and classify matrices
• Master the fundamental concepts of abstract vector spaces
• Decompose linear transformations and analyze their spectra (eigenvectors and eigenvalues)
• Apply orthogonal projection to optimization (least-squares) problems

The material we take up in this course has applications in physics, chemistry, biology, environmental science, astronomy, economics, and statistics. We want you to leave the course not only with computational ability, but with the ability to use these notions in their natural scientific contexts, and with an appreciation of their mathematical beauty and power. Prerequisites: Multivariable Calculus and departmental approval.

How can you use the formulas for the areas of traditional plane figures to find the areas of nontraditional plan figures?
How does the concept of similarity lead to trigonometry and proportions in a circle?

Geometry is a hands-on course in which students will explore the concepts of Euclidean geometry. This class also integrates the study of important algebra topics to prepare students for Algebra II. Throughout the year, students will use geometric tools and various manipulatives to discover and demonstrate geometric properties. Students will use computer programs, iPad apps and rulers, compasses, and protractors to complete projects and explore concepts. These concepts include the properties of parallel lines, the Pythagorean Theorem, right triangle trigonometry, area, volume, and the many interesting properties of circles. By the end of the course, students will have explored the basics of Euclidean geometry and will be prepared for Algebra II.

What is proof? How do you use deductive reasoning to demonstrate the validity of previously accepted ideas?
How can you use the formulas for the areas of traditional plane figures to find the areas of nontraditional plane figures?
How does the concept of similarity lead to trigonometry and proportions in a circle?

This course covers geometric theory, its methods and applications. A careful development of deductive reasoning is presented and students will use two-column proofs to prove many important theorems and properties. Students will also use computer programs, iPad apps and rulers, compasses, and protractors to complete projects and explore concepts. These concepts include the properties of parallel lines, the Pythagorean Theorem, right triangle trigonometry, area, volume, and the many interesting properties of circles. By the end of the course, students will have thoroughly explored Euclidean geometry and will be prepared for Algebra II.

How can one use trigonometric functions to model real world phenomena?
How do small changes transform exponential and polynomial functions?
How can one best use a graphing calculator and other technology to gain a deeper understanding of mathematics?

In addition to reviewing some basic algebra skills this course covers functions (e.g. linear, quadratic, exponential) in great detail, with a strong emphasis on trigonometric functions and their applications. Additional topics include conic sections, exponential growth and decay, probability, and statistics.

Why do certain functions model data better than others?
How can basic functions be transformed to represent complicated phenomena?
How can graphing calculators lead us astray?
Continuous functions vs. discrete mathematics: what, when, why?

This course expands the study of applications of polynomial, exponential, logarithmic, and trigonometric functions. Additional topics include sequences, series, conic sections, polar graphs, probability, and statistics. Students who successfully complete this course are prepared for the study of calculus.

Why do certain functions model data better than others?
How can basic functions be transformed to represent complicated phenomena?
How can graphing calculators lead us astray?
Continuous functions vs. discrete mathematics: what, when, why?

This course expands the study of applications of polynomial, exponential, logarithmic, and trigonometric functions. Additional topics include sequences, series, conic sections, polar graphs, probability, and statistics. Students who successfully complete this course are prepared for the study of calculus. Advanced level mathematics classes spend less time reviewing foundational material and investigate many topics at a greater depth than standard classes.

What roles do zero and infinity play in mathematics?
What can derivatives and integrals tell us about functions?
What previously unapproachable problems are now very solvable using calculus?

Through multiple representations and extensive use of technology, this course develops the concepts and methods of differential and integral calculus. These results are applied to problems involving related rates of change, optimization, area, volume, and distance.

What roles do zero and infinity play in mathematics?
What can derivatives and integrals tell us about functions?
What previously unapproachable problems are now very solvable using calculus?

This is a college-level mathematics course. Through multiple representations and extensive use of technology, the class rigorously develops the concepts and methods of differential and integral calculus, including transcendental functions. These results are applied to problems involving related rates of change, optimization, area, volume, and distance.

This course extends the ideas from Calculus I to functions of two or more variables. Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2- and 3-space.

Functions of two or more variables are interesting in their own right, but they are also essential for describing the physical world. Many things depend on more than one independent variable. Here are just a few:

• In thermodynamics, pressure depends on volume and temperature.
• In electricity and magnetism, the magnetic and electric fields are functions of the three space variables (x,y,z) and one time variable t.
• In economics, functions can depend on a large number of independent variables, e.g., a manufacturer's cost might depend on the prices of 27 different commodities.

How can statistics be used to predict the future and how certain can we be about our predictions?
How do we use a sample to make inferences about a population and when can we trust those inferences?

In this year-long course, students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The topics are divided into four major themes: exploratory analysis, planning a study, probability, and statistical inference.