**M-125 Algebra I**

Year 1 unit

In this course, students expand their notion of a variable and connect it to algebraic and problem-solving techniques. This is a comprehensive course that lays the foundation for both Algebraic Geometry and Algebra II and Trigonometry. Topics include signed numbers, radicals and radical operations, linear equations, systems of linear equations, exponents, the quadratic formula, polynomials, and factoring. Students in this course learn to translate verbal statements into mathematical statements, clarify procedural questions, solidify arithmetic skills, and comprehend the abstraction of the coordinate plane. Class time is used for discussion, developing initiative in problem-solving and perfecting study skills.

Open to: 9/10

**M-225 Algebraic Geometry**

Year 1 unit

This course uses a problem-based curriculum that enables students to investigate and prove geometric concepts. Topics include distance in a coordinate plane, the Pythagorean Theorem, angles, parallel and perpendicular lines, planes, vectors, properties of triangles, properties of quadrilaterals, regular polygons, transformations, congruence, similarity, right triangle trigonometry, circles, area, perimeter, volume, and surface area. Proficiency in basic algebra is expected and necessary. Geometry students are active learners, engaging the problem-solving skills learned in Algebra I. The course stresses the connections between algebra and the geometric topics covered. Each student develops the practice of self-assessment so that she is better able to critique her understanding. Class discussion centers around problem sets, and students employ graphing calculators, dynamic computer software, the Internet, and journals as tools in the learning process.

**Prerequisite:** Algebra I (M-125)

Open to: 9/10/11

**M-325 Algebra II and Trigonometry**

Year 1 unit

This course continues to develop independent problem-solving skills while expanding those skills to solve, graph and interpret linear, absolute value, and quadratic equations, as well as higher-degree polynomial functions, inverse functions, exponential functions, logarithmic functions, rational functions, and trigonometric functions. Functions introduce an abstract thought process, and the focus is on solving problems and reading carefully in order to build skills. At this level, students are expected to reason independently and formulate questions based on insights into applications of the algebra previously studied.

**Prerequisite: **Algebraic Geometry (M-225)

Open to: 9/10/11/12

**M-326 Algebra II and Trigonometry with Non-Routine Problems**

Year 1 unit

This course continues to develop independent problem-solving skills while expanding those skills to solve, graph and interpret linear, absolute value, and quadratic equations, as well as higher-degree polynomial functions, inverse functions, exponential functions, logarithmic functions, rational functions, and trigonometric functions. Functions introduce an abstract thought process, and the focus is on solving problems and reading carefully in order to build skills. At this level, students are expected to reason independently and formulate questions based on insights into applications of the algebra previously studied. Students will spend a substantial amount of time studying applications of functions to real-life, non-routine problems.

**Prerequisite: **Algebraic Geometry (M-225)

Open to: 9/10/11/12

**M-430 College Algebra and Its Applications**

Year 1 unit

This course explores four major units: functions and their graphs, with an emphasis on transforming functions; exponential and logarithmic functions; trigonometry and trigonometric graphs; and logic, reasoning, and SAT prep, which includes a substantial geometry review. In between these major units, and woven throughout the course, students complete mini-projects and read books that apply math to daily life. Although the course is based on traditional algebraic and graphical problem solving, it emphasizes real-world applications wherever possible, including log-log plots, harmonic motion, circular motion, logistic curves, and population growth. Students solve problems daily and keep a semi-weekly mathematical journal. Students who take this course may take Precalculus the following year.**Prerequisite:** Algebra II and Trigonometry (M-325) or Algebra II and Trigonometry with Non-Routine Problems (M-326) and recommendation of the department

Open to: 10/11/12

Open to: 10/11/12

**M-440 Statistics with Discrete Math**

Year 1 unit

In today’s data-driven world it is becoming increasingly necessary to have a knowledge of statistics in a wide variety of fields including medicine, pharmacology, engineering, finance, insurance and the social sciences. This elective course is designed for those students who are interested in studying statistics at a deeper level in preparation for AP Statistics or an introductory college statistics course. During the first semester we cover statistics, including sampling techniques, descriptive and inferential statistics including measures of center and spread, and the standard normal curve and z-scores. During the second semester we cover set theory, combinatorics, probability, regressions, and a unit on personal finance, including the cost of borrowing money. If time allows, voting and apportionment methods in U.S. history are studied. Assessments include tests and quizzes as well as two major projects that incorporate the use of a spreadsheet, research into the topic of study and writing about the statistics.**Prerequisite:** Algebra II and Trigonometry (M-325) or Algebra II and Trigonometry with Non-Routine Problems (M-326) and recommendation of the department

Open to: 10/11/12

Open to: 10/11/12

**M-450 Precalculus with Statistics**

**Year 1 unit**

This course is designed for students who have completed the study of basic trigonometry and algebra. In Precalculus, students are introduced to different areas of study in higher-level mathematics. Topics include advanced trigonometry, vectors and their applications to physics, functions, modeling, statistics, analytic geometry, series, and limits. The course assumes that students employ effective questioning skills: not just procedural, but analytical. In addition, students apply a range of methods when problem solving. This course involves significant independent work, and students are responsible for assessing their progress and seeking help in the Math Learning Center as necessary.

**Prerequisite**: Algebra II and Trigonometry (M-325) or Algebra II and Trigonometry with Non-Routine Problems (M-326) and recommendation of the department

Open to: 10/11/12

Open to: 10/11/12

**M-460 Precalculus with Non-Routine Problems**

Year 1 unit

This course is designed for students who have successfully completed the study of trigonometry and algebra. Students study the various topics of precalculus which include advanced trigonometry, vectors and their applications to physics, functions, probability, statistics, analytic geometry, limits, complex numbers, polar coordinates, polynomial theorems, and sequences and series. In addition, students examine a large number of non-routine problems which require creative problem-solving skills. The successful student in this course is proactive both in and out of the classroom, seeks help when necessary, works independently, uses effective questioning skills, frequently enters into or initiates discussions in class, and has a natural curiosity to pursue not only the mechanics of problem-solving but also the concepts behind the problem. She also readily draws from a variety of problem-solving skills.

**Prerequisite**: Algebra II and Trigonometry (M-325) or Algebra II and Trigonometry with Non-Routine Problems (M-326) and recommendation of the math department

*Open to: 10/11/12*

**M-500 Calculus**

Year 1 unit

This course is designed for students looking for a moderately paced course in calculus. The course covers the traditional topics of differential and integral calculus with special emphasis on applications, and it prepares students well for college and/or continued study in mathematics. This course is not intended to prepare students for the AP Calculus examination.

**Prerequisite**: Precalculus (M-450) or Precalculus with Non-Routine Problems (M-460) and recommendation of the department

Open to: 11/12

**M-540 Advanced Placement Statistics**

Year 1.5 units

This course offers a thorough examination of data analysis, data production, and statistical inference. Topics include the normal distribution, correlation and regression, experimental design, sampling distributions, probability theory, confidence intervals, tests of significance, and the Chi-Square Test. Diverse areas such as economics, medicine, and politics are incorporated into discussions of statistical topics. Solution methods for the Advanced Placement exam and assessments in this class employ technology. Also, students should expect significant reading, written analysis, and interpretation as parts of statistical inference. As with other AP courses, additional assignments should be expected over school vacations, and summer work is required. Students in this course are required to sit for the AP Statistics exam in May.**Prerequisites:** Precalculus (M-450) or Precalculus with Non-Routine Problems (M-460) and recommendation of the department

Open to: 11/12

Open to: 11/12

**M-550 Advanced Placement Calculus AB**

Year 1.5 units

This course prepares students for the AP Calculus AB exam. It offers a thorough exposure to differential and integral calculus. The course begins with a review of functions and their graphs, followed by derivative functions, limits, continuity, and the definite integral. Derivative rules and applications complete the study of differential calculus, and this is followed by additional work with integrals and their applications. The course finishes with the topics of differential equations and slope fields. All students who take this course are required to take the AP Calculus AB exam in May. As with other AP courses, additional assignments should be expected over school vacations, and summer work is required.

**Prerequisites:**Precalculus (M-450) or Precalculus with Non-Routine Problems (M-460) and recommendation of the department

Open to: 11/12

Open to: 11/12

M-565 Advanced Placement Calculus C

M-565 Advanced Placement Calculus C

Fall .75 units

This course is a continuation of AP Calculus AB (M-550) and covers only those topics on the College Board BC topic outline not already presented in Calculus AB. These include integration by parts and by partial fractions, improper integrals, curve length, infinite series, and parametric and polar functions. All students are required to sit for the AP Calculus BC exam in May. In preparation for this exam, there are several weeks of required review sessions in the spring. Students should also expect a substantial summer assignment and possible assignments during school vacations.

**Prerequisites:**AP Calculus AB (M-550) and recommendation of the department

Open to: 11/12

Open to: 11/12

**M-570 Multivariable Calculus**

Spring .75 units

This course covers topics that are typically offered in a third-semester college course in multivariable calculus. These include vectors and surfaces in three-dimensional space, vector-valued functions, partial derivatives, vector fields, and line integrals. This is a particularly helpful course for students who plan to study engineering, physics, or math in college.**Prerequisite:** Advanced Placement Calculus C (M-565) and recommendation of the department

Open to: 11/12

Open to: 11/12

**Online School for Girls Course Offerings**

Emma Willard offers one Online School for Girls course at no additional cost to Emma Willard students as long as the course is taken as one of a student’s six-course load. An Online School for Girls course taken in addition to a student’s regular course load will be taken at the expense of the student. Tuition for Online School for Girls courses for 2016/17 is $1,495 for a year-long course.

**Online School for Girls: Linear Algebra**

Year 1.5 Unit

Linear algebra is the study of vectors, the spaces in which they live, and linear mappings between those spaces. It gives us a powerful new way to think mathematically, and it has many applications in science, engineering, economics, and any field in which multiple variables interact in ways that can be modeled by systems of linear equations. It’s therefore a required and very useful subject in college for many science and engineering majors. This year-long course covers a typical one-semester college linear algebra curriculum, with topics including matrix algebra, vector spaces, eigenvalues and eigenvectors, and applications to differential equations. In the sequence of standard math courses, linear algebra can be studied either before or after multivariable calculus. It’s a great fit for the student who has completed AP Calculus AB or BC, who is passionate about challenging herself to think in new ways, and who wants to increase her ability to tackle problems in the real world.

Prerequisite*:** *Successful completion of Advanced Placement Calculus C (M-565) and Multivariable Calculus (M-570)

Open to: 9/10/11/12