CAA mathematics and computer science courses offer students the opportunity to strengthen their problem-solving skills and to explore challenging material. These courses ask students not only to master concepts and theoretical material, but also to apply their new knowledge to real-world questions and problems. Through hands-on approaches and thought-provoking exercises, students learn to make connections between abstract ideas and their use in a range of fields, including science, engineering, and advanced mathematics. Please refer to the Eligibility section of this catalog for minimum test score requirements for math courses. Sample syllabi for all courses are also available.
Mathematical Modeling
Mathematics is more than just numbers and symbols on a page. It can be used to determine whether a meteor will impact Earth, predict the spread of an infectious disease, or analyze a remarkably close presidential election. Applications of mathematics are indispensable in the modern world. In this course, students learn how to create mathematical models to represent and solve problems across a broad range of disciplines, including political science, economics, biology, and physics. Students investigate voting systems by constructing mathematical models of how groups make decisions and how elections are decided. They consider how goods, property, and even political power can be fairly divided and apportioned. Students learn how to use Euler and Hamilton circuits to find the optimal solutions in a variety of real-world situations, such as determining the most efficient way to schedule airline travel. In investigations of growth and symmetry, students develop linear and exponential growth models and explore fractals and the Fibonacci numbers. Students leave this course with the ability to use the seemingly abstract language of mathematics to make the world in which we live a better place. Note: A graphing calculator, such as a TI-83, is recommended. Sample text: Excursions in Modern Mathematics, Arnold and Tannenbaum. Session 1: Bristol, Easton, Santa Cruz
Session 2: Easton, Santa Cruz Top
The Mathematics of Money
From managing one’s personal investments to examining the profitability of a multibillion-dollar global corporation, the mathematics of money is at the heart of successful financial endeavors. Why are round-trip fares from Orlando to Kansas City higher than those from Kansas City to Orlando? How do interest rate adjustments made by the Federal Reserve affect the real estate market? How does one calculate the price-earnings ratio of a stock and use that to help predict that stock’s future performance? Mathematics is an indispensable part of the answer to each of these questions. This course provides students with a rigorous, mathematical grounding in central concepts of business and finance. Students investigate the mathematics of buying and selling, and apply these principles to real world situations. They gain fluency with the concepts of simple and compound interest and learn how these affect the present and future value of loans, mortgages, and interest bearing accounts. Students also explore stocks and bonds and acquire a firmer understanding of national and international financial markets. In their examination of these topics, students manipulate and solve algebraic expressions, as well as learn to apply a range of mathematical concepts including direct and indirect variation and arithmetic and exponential growth. Through simulations, projects, and classroom investigations, this course not only provides students with the foundation required to be more secure in their own personal financial management, but also starts them on the road to becoming the leading financiers and entrepreneurs of the twenty-first century. Sample texts: New course. Session 1: Bethlehem, Santa Cruz, Thousand Oaks
Session 2: Bethlehem, Bristol, Santa Cruz, Thousand Oaks
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Geometry and Its Applications
The word “geometry” means “earth measurement.” It is the branch of mathematics most strongly connected to the physical world. Therefore, it has many applications to problems encountered in everyday life by every culture, past and present. Long before Pythagoras introduced his famous theorem, ancient Egyptians used geometry to form right angles to resurvey the Nile River Valley after the annual floods. Today, NASA scientists use the same formulas and theorems to determine the proper angles and arcs for the orbital paths of modern telecommunications satellites. In this course, designed as an introduction to geometry, students learn about geometric figures, properties, constructions, and proofs, with an emphasis on their wide applicability to human activity. Concepts are studied in depth through practice exercises and problem-solving activities. Students are exposed to many examples in which geometry is used in recreation, practical tasks, science, and the arts. While this course covers conceptual material, the focus is on applying geometry to solve problems and on discovering the importance of mathematics in a wide range of disciplines and situations. Note: This course is recommended as preparation for students who plan to take Geometry at school. Students should not use this course to replace a geometry course at their schools. Students are exposed to geometric properties and concepts, but due to the focus on applications they do not cover the breadth of material found in a year-long geometry course. Sample text: Discovering Geometry: An Inductive Approach, Serra. Session 1: Bethlehem, Bristol, Easton, Santa Cruz, Thousand Oaks
Session 2: Bethlehem, Bristol, Easton, Santa Cruz, Thousand Oaks Students who have already taken Geometry should not take this course. Top
Discrete Math
Can any given map be colored with just four different colors such that no two regions sharing a common edge are the same color? Mathematicians took more than 100 years to demonstrate this is possible and thus prove the Four-Color Theorem. Such questions are the domain of discrete math, a field that examines objects that have values characterized by natural numbers. This course focuses on two core areas within discrete math: combinatorics and graph theory. Students begin by building a foundation in set theory, induction, and proof construction. They then explore combinatorics, examining the number of possible configurations of different sets of objects. Even when the conditions specified for a configuration are relatively simple, counting the possibilities often requires great ingenuity. Combinatorics lays the groundwork for investigations in diverse areas of higher mathematics, including probability, optimization, and number theory. Students discover natural applications for enumeration techniques when they delve into graph theory, a subject rich in abstract concepts, such as counting and coloring theorems, and in applications, such as traffic networks, models for molecules, and link structures for websites. Unlike familiar graphs of equations, graph theory focuses on objects and the connections between them. Students leave the course with an enriched mathematical vocabulary, a familiarity with a flourishing branch of mathematics, and an ability to understand and create original mathematical arguments. Sample text: Materials compiled by the instructor. Prerequisite: Algebra I or a CAA math course. Session 1: Easton, Santa Cruz
Session 2: Not offered Top
Chaos and Fractals
Can a small action in one part of the world lead to catastrophic consequences in another? Can order be revealed in chaos? For mathematicians the quest to understand and structure the unpredictable dates back to the 1890s and the renowned French mathematician Henri Poincaré. Chaos theory today is an important area of study with a wide range of applications in the physical and social sciences as well as the arts. In this course, students investigate the mathematical foundations of chaotic dynamical systems and fractals. They begin by learning the fundamental process of iteration in functions. With that foundation, they examine more advanced concepts including bifurcations and sensitive dependence. Linking this abstract mathematics with the real world, students explore applications of chaos theory such as forecasting weather, understanding purchasing power and world markets, or examining heart arrhythmia. Students apply their knowledge of iterated functions and chaotic systems to investigate the origins and applications of fractals, geometric patterns which exhibit some degree of self-similarity at any scale. Such fractals may include the Cantor set and the Mandelbrot set. Through these topics students gain a more formal understanding of the basic principles of chaos theory, an area of math usually studied only by undergraduate and graduate students. Sample text: Materials compiled by the instructor. Prerequisite: Algebra I. Session 1: Not offered
Session 2: Easton, Santa Cruz Top
Foundations of Programming
Students in this course gain insight into the methods of computer programming and have an opportunity to study the algorithmic aspects of computer science. They learn the theoretical constructs common to all languages by studying the syntax and basic commands of a particular programming language. Building on this knowledge, students move on to study additional concepts of programming, including arrays, testing, and debugging. Students are given a variety of challenging problems which teach them to start with a concept and work through the steps of writing a program: defining the problem and its desired solution, outlining an approach, encoding the algorithm, and debugging the code. Through a combination of individual and group work, students complete supplemental problems, lab exercises, and various programming projects in order to reinforce concepts learned in class. By the end of the course, students are able to develop more complex programs and are familiar with some of the standards of software development practiced in the professional world. Students leave with an understanding of how to apply the techniques learned to other programming languages. Note: Students who have taken CAA’s Computer Science: Introduction to Programming should not take this course. Sample text: An introductory computer programming text. Lab Fee: $65 Session 1: Bethlehem, Bristol, Easton, Thousand Oaks
Session 2: Bethlehem, Bristol, Easton, Thousand Oaks Top
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