# Magnet Courses

## Magnet Geometry

• Prerequiste: attainment of the outcomes of Algebra 1
• 0.5 credit per semester

If triangles are the things for you, Magnet Geometry is the place to be. From logic to the law of cosines, this class covers it all. You can follow in the steps of Euclid as you prove the major geometric theorems from the basic to the mind-boggling. Or learn your if's, and's, and or's as you work through rigorous logic proofs. In the end, Magnet Geometry provides an engaging learning experience and a rock-solid foundation for the math and life to come.

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Students study logic, methods of proof (direct/indirect, coordinate) in both two-column and essay forms, constructions, loci, and transformational geometry. All of the objectives of the MCPS Honors Geometry curriculum are taught. Nontraditional topics studied include affine geometry, conics, circuit diagrams, writing a two-bit adder on a circuit board, and an introduction to circular functions.

## Magnet Precalculus A, B, C

• Grade Level: 9 - 10 - 11
• Prerequisite for Precalculus A, B: Attainment of the outcomes of Magnet or Honors Geometry and teacher recommendation
• Prerequisite for Precalculus C: Attainment of the outcomes of Magnet Precaculus A and B
• 0.5 credit per semester

The starting grounds for most of the students in the Magnet Program, Precalculus will provide students the basics for future Magnet math courses, such as Analysis 1 and Analysis 2. In Precalculus A, students will begin to learn functions and their properties, as well as introductory trigonometry. As a continuation of the math curriculum, the Precalculus B and C courses will expand students' horizons in solving various equations, and learning about vectors, polar coordinates, conics, and series and sequences. Although the information presented in Precalculus is a lot of ground to cover in two or three semesters, students will be well-prepared for math in their future years.

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The properties of the real numbers and of functions, and the solution of equations in one variable are introduced. The discussion of functions includes all forms of algebraic, exponential, logarithmic, and circular functions. The study of each function includes a precise definition, a consideration of graphs and applications, an analysis of distinguishing features, and an identification of related tangents and slope.
The definition, properties,and application of matrices are studied. The discussion of functions includes all forms of algebraic, exponential, logarithmic, and circular functions. The study of each function includes a precise definition, a consideration of graphs and applications, an analysis of distinguishing features, and an identification of related tangents and slope.

## Magnet Functions A/B

• Grade Level: 9 - 10
• Prerequisite: Teacher recommendation and the attainment of the outcomes of Magnet or Honors Geometry
• 0.5 credit per semester

Functions is by invitation only. The curriculum is very similar to the Precalculus A, B, and C courses, but Functions is an intense, two-semester course whereas Precalculus is taught over three semesters.

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Functions begun in Algebra 1 are continued and expanded to include all forms of algebraic, exponential, logarithmic, and circular functions. The study of each includes a precise definition, a consideration of graphs and applications, an analysis of distinguishing and interesting features, and an identification of related tangents and slopes. Students study trigonometry, approached from circular functions, conics, limits, and derivatives.

## Magnet Analysis 1A/B

• Grade Level: 10 - 11 - 12
• Prerequisite: Attainment of the outcomes of Magnet Precalculus or Magnet Functions
• 0.5 credit per semester

Boiled down to one sentence, calculus is simply the study of change. But what makes calculus so powerful is the elegant concept of limits that drives it at its core. By taking everything you've learned in math so far and mixing it up with the magic of limits, a new world of theoretical and applicable results opens up. Soon after covering the basics of derivatives and integrals, you'll be able to chug away with "The Limit Machine" on some of the fundamental concepts from physics to economics. Plus, in the Magnet we call this course Analysis because it covers a lot more information than a normal high-school calculus course.

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The delta-epsilon definition of the limit of a function is examined and applied to develop the ideas of differentiation and integration. All the nonvector objectives of the MCPS AP calculus curriculum are studied with a greater degree of rigor and sophistication. Students study infinite series, differential equations, and the analysis of the polar plane. Students apply this knowledge to solve problems in the sciences and economics. Students take the AP Calculus BC Exam after completing this course.

## Multivariable Calculus and Differential Equations A/B (Magnet Analysis 2)

• Grade Level: 11 - 12
• Prerequisite: Attainment of the outcomes of AP Calculus BC with teacher recommendation.
• 0.5 credit per semester

So you've taken Analysis 1, and you've mastered change in one variable. But how do you deal with problems in the real world that deal with change in all three dimensions? That's where Analysis 2 comes in. In this course you'll learn how to extend some of the concepts from Analysis 1 to into multiple dimensions, leading to deep connections in fields as varied as electromagnetism to weather patterns. In the second semester of the course you'll cover methods of solving differential equations used to describe various forms of motion.

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The first semester covers three-dimensional analytic geometry and vectors; the calculus of functions of more than one variable, including partial derivatives, vector-valued functions, multiple integrals, volumes, surface area, and the classical theorems of Green, Stokes, and Gauss. The second semester introduces the basic concepts of ordinary differential equations.

## Applied Statistics

• Grade Level: 11 - 12
• Prerequisite: Attainment of the outcomes of Magnet Analysis 1, AP Calculus BC, or teacher recommentation.
• 0.5 credit per semester

Mark Twain once wrote that "There are three kinds of lies: lies, damned lies, and statistics." Twain was right that numbers are manipulated all the time to support every claim, but the harshness of his cynicism may have resulted from his incomplete understanding of true, mathematical statistics. Far from the stereotype of con men rattling off questionable numbers, statistics is in fact a mathematically rigorous and intellectually rich field of research. In addition to learning how to spot flaws in real-life statistical attempts, in this course you'll cover the potential sources of bias in a study, the proper procedures for setting up statistically-sound experiments, and the correct methods for analyzing various types of data. Besides providing a mathematical understanding of statistics, this course is also useful when designing and analyzing experiments during the Senior Research Project experience.

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Students learn sufficient statistical background to design, collect, and analyze data for surveys and research projects. All the objectives of the MCPS AP statistics curriculum are studied with a greater degree of rigor and sophistication. Students study simple probability theory, counting techniques, and a variety of probability distributions. These distributions justify tests of significance of parametric and nonparametric statistics.

## Discrete Mathematics

• Grade Level: 11 - 12
• Prerequisite: Attainment of the outcomes of Magnet Precalculus or Functions and Analysis of Algorithms or AP computer science
• 0.5 credit per semester

Most of your mathematics education in school has probably been focused on continuous mathematics, with geometrical shapes that form perfectly connected curves and functions that can be applied all across the real numbers. But what about phenomena that are fundamentally discrete, that involve counting distinct objects with separate numbers rather than on a continuum? Discrete mathematics tries to fit this entire half of mathematics into a single course, focusing on concepts from areas such as combinatorics, graph theory, and logic, paying special attention to applications in computer science.

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Students learn the mathematical tools, language, and thought processes used in computer science. The analysis of finite collections of objects provides a solid foundation in set and graph theory. Students study combinations, countability, and number theory to establish the framework for analysis of data structures. Matrices and matrix algebra are studied to describe and manipulate graphs.

## Linear Algebra

• 0.5 credit per semester
• Grade Level: 11 - 12
• Prerequisite: Attainment of the outcomes of Magnet Analysis I or teacher recommendation

Linear Algebra is a field that deals with vectors, matrices, and spaces. You may think that these concepts sounds way too abstract, but in fact linear algebra may be one of the most applicable and foundational fields in mathematics. Besides being used to formalize a variety of fundamental ideas in mathematics, linear algebra is connected to a variety of computer applications, from computer graphics to network algorithms. In fact, the basic ideas used in modern search engines like Google are rooted in linear algebra.

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Students learn the theory and practice of matrices and determinants and their use in solving linear equations. They study the structure and properties of linear transformations, vector spaces, and linear programming as they apply to such fields as biology, chemistry, differential equations, economics, psychology, and weather forecasting.

## Complex Analysis

• 0.5 credit per semester
• Grade Level: 11 - 12
• Prerequisite: Attainment of the outcomes of Magnet Analysis 2

You may know that complex numbers arise when you play around too much with square roots and negative numbers. However, complex numbers aren't just curiosities resulting from bad mathematical behavior. The most advanced calculus class offered in the Magnet, Complex Analysis takes the concepts from the first two Analysis courses a step further by pushing them into the exotic realm of the complex plane. In this course you'll study some of the concepts that are being applied to the hottest problems in mathematics and physics today, such as the Riemann Hypothesis and string theory.

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Students are introduced to the theory of functions of complex variables, an essential part of the mathematical background of engineers, physicists, mathematicians, and other scientists. They review complex numbers and study complex functions and the calculus of complex functions, including derivatives and integrals. Other topics studied include series, residues, and conformal mappings.