Mathematics and Computer Science

Every student is required to take mathematics each year. Students new to Moravian Academy may be required to take a placement test. Students must earn at least a C- in order to continue in the mathematics sequence. The Mathematics Department does not typically recommend summer courses in place of courses taken during the regular school year. Students who have a strong interest in mathematics are encouraged to enroll in summer enrichment opportunities. A list of summer programs is available at the Upper School College and Summer Enrichment portion of Moravian Academy’s website. Some of the programs that talented math students have participated in recently include: Boston University PROMYS - Mathematics for Young Scientists; Smith College - Summer Science and Engineering for Girls; Stanford University Mathematics Camp; Hampshire College Summer Studies in Mathematics. The American Mathematical Society has a listing of summer programs at http://www.ams.org/programs/students/high-school/emp-mathcamps; from Program in Mathematics for Young Scientists http://mathforum.org/students/high/opps.html

The following is the sequence of math courses for Moravian Academy students:
Algebra I
Algebra II or Algebra II Honors
Geometry or Geometry Honors

After Geometry, students are placed in the appropriate courses chosen from the following electives:
Precalculus or Precalculus Honors
Probabilty and Statistics
Calculus or AP Calculus (AB or BC)
AP Probability and Statistics
AP Computer Science Principles
AP Computer Science A
Calculus II or Calculus II Honors
Linear Algebra Honors
Introduction to Computer Programming I
Introduction to Computer Programming II

Algebra I

2 Semesters, 1.0 Credit, Full-Time

An introduction to modern algebra. Topics include: polynomials in one and two variables, solutions of linear equations and inequalities, linear functions and graphing, systems of two equations in two unknowns, rational algebraic expressions, quadratic equations solved by factoring and the quadratic formula, proportions and percents, irrational numbers, and application problems.
Algebra II

2 Semesters, 1 Credit, Full Time Course

A continuation from the Algebra I study of linear equations. Topics include: linear systems and inequalities, the complex number system, irrational and imaginary numbers, rational and polynomial expressions, linear, rational, and quadratic functions, including their graphs, and methods for solving equations. Students in this course are expected to purchase a TI-84 graphing calculator.
Prerequisite: Students are eligible if they have successfully completed Geometry or Geometry Honors.
Algebra II Honors

2 Semesters, 1 Credit, Full Time Course

A rigorous and fast-past continuation from the Algebra I study of linear equations. Topics include: linear systems and inequalities, the complex number system, irrational and imaginary numbers, rational and polynomial expressions, linear, rational, and quadratic functions, including their graphs, and methods for solving equations. An exposure to exponential and logarithmic functions as well as sequences and series will be included. Students in this course are expected to purchase a TI-84 graphing calculator. Prerequisite: Students are eligible if they have earned a B+ or higher in Geometry Honors or an A- or higher in Geometry.
AP Calculus AB

2 Semesters, 1 Credit, Full Time Course (Grades 10-12)

Curriculum for this course follows the AP Calculus AB curriculum set by the College Board and is designed to prepare students for the AP Calculus AB exam in May. The course covers Differential Calculus in the first semester and Integral Calculus in the second semester, with emphasis on graphical, numerical, and analytical methods. Topics include: the derivative, function analysis and curve sketching, optimization, anti-derivatives, definite integrals and area under a curve, volumes of solids, differential equations, and applications of calculus. The graphing calculator is used throughout. Students in this course are expected to purchase a TI-84 graphing calculator. Prerequisite: Students are eligible if they have earned either a B+ or higher in Precalculus Honors or an A or higher in Calculus.
AP Calculus BC

2 Semesters, 1 Credit, Full Time Course (Grades 10-12)

Curriculum for this course follows the AP Calculus BC curriculum set by the College Board and is designed to prepare students for the AP Calculus BC exam in May. This is a rigorous course covering the topics included in the AP Calculus AB course in greater detail and completely covering the calculus of a single variable. Additional topics include: properties of functions given in parametric, polar, and vector form, more applications of integrals and integration techniques, and a thorough study on infinite series. Students in this course are expected to purchase a TI-84 graphing calculator.
Prerequisite: Students are eligible if they have earned an A or higher in Precalculus Honors.
AP Computer Science A

2 Semesters, 1 Credit, Full Time Course (Grades 10-12)

Curriculum for this course follows the AP Computer Science A curriculum set by the College Board and is designed to prepare students for the AP Computer Science A exam in May. This course introduces students to computer science through programming. Fundamental topics in this course include the design of solutions to problems, the use of data structures to organize large sets of data, the development and implementation of algorithms to process data and discover new information, the analysis of potential solutions, and the ethical and social implications of computing systems. The course emphasizes object-oriented programming and design using the Java programming language.
Prerequisite: Students are eligible if they have successfully completed Algebra II or Algebra II Honors and have either earned a B+ or higher in a computer science course or earned a score of B or higher on the AP Computer Science A qualification project.
AP Computer Science Principles

2 Semesters, 1 Credit, Full Time Course (Grades 10-12)

Curriculum for this course follows the AP Computer Science Principles curriculum set by the College Board and is designed to prepare students for the AP Computer Science Principles exam in May. This course is designed to be equivalent to a first semester introductory college computing course. Students will learn the foundational concepts of computer science and explore how computing and technology impact the world. The course will provide the fundamentals of computing, including problem solving, working with data, understanding the Internet, cybersecurity, and programming. Students will also develop effective communication skills while working individually and collaboratively to solve problems. The AP exam includes a written test and the submission of a performance task to the College Board.
Prerequisite: Students are eligible if they have successfully completed Algebra I.
AP Statistics

2 Semesters, 1 Credit, Full Time Course

Curriculum for this course follows the AP Statistics curriculum set by the College Board and is designed to prepare students for the AP Statistics exam in May. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. Additionally, using the vocabulary of statistics, this course will teach students how to communicate statistical methods, results and interpretations. Students will learn how to use graphing calculators and read computer output in an effort to enhance the development of statistical understanding. Students will use a graphing calculator in this course.
Prerequisite: Students are eligible if they have successfully completed Algebra II Honors, Precalculus, or Precalculus Honors. A score of 2 or higher on the FRQ writing sample is also required.
Calculus

2 Semesters, 1 Credit, Full Time Course

This is an introductory calculus course. Topics include: limits, the derivative, tangents to the graph of a function, optimization analysis, curve sketching, anti-derivatives, and area under a curve. Other advanced topics may be explored as time permits. Upon completion of this course, students should be able to successfully complete a college-level calculus course. Students in this course are expected to purchase a TI-84 graphing calculator.
Prerequisite: Students are eligible if they have successfully completed Precalculus or Precalculus Honors.
Calculus II Honors-S1

1st Semester, .5 Credit, Full Time Course (Grades 11-12)

A continuation of the AP Calculus AB syllabus, covering those topics in the BC course not covered in the AB course. Topics include: further techniques and applications of integration, improper integrals, differential equations, infinite series, and functions given in parametric, polar, and vector form. If time allows, further vector topics will be considered. Students enrolled in this course will take the AP Calculus BC exam in May. Students in this course are expected to purchase a TI-84 graphing calculator. Prerequisite: Students are eligible if they have earned a B+ or higher in AP Calculus AB and a score of 3 or higher on the AP Calculus AB exam.
Calculus III Honors-S2

2nd Semester, .5 Credit, Full Time Course (Grades 11-12)

A continuation of the foundation of topics developed in AP Calculus BC. Topics will include vector algebra, vector calculus, partial derivatives, gradients and directional derivatives, tangent planes, multiple integrals, and line integrals.
Students in this course are expected to purchase a TI-84 graphing calculator.

Prerequisite: Minimum grade of B- in AP Calculus BC with a grade of 3 or more on the AP Calculus BC exam or minimum grade of B- in Calculus II Honors
Cybersecurity Honors

2 Semesters, .5 Credit, Part Time Course (Grades 11-12)

The overarching goal of this course is to introduce students to the foundational concepts, principles, and tools of cybersecurity. Cybersecurity Honors lays a foundation for understanding cyber law and policy, Linux, networking technology basics, risk assessment, cryptography, and a variety of cybersecurity tools – all the essential knowledge and skills needed to begin a future in the cybersecurity workforce.

Prerequisite: Students are eligible if they have successfully completed AP Computer Science A.
Geometry

2 Semesters, 1 Credit, Full Time Course

Euclidean plane geometry is the focus of this course. There will also be an introduction into the basic concepts of Probability and Statistics. Geometric topics include: basic undefined terms, formal and informal definitions, deductive reasoning, parallel lines, congruent triangles, quadrilaterals, similar triangles, right triangles and the Pythagorean theorem, right triangle trigonometry, circles, and areas and volumes of plane and solid figures. Probability and Statistics topics include: presenting data, analyzing data, normal distributions, correlation, permutations, combinations, probability, mutually exclusive and independent events. In addition, algebra topics are reviewed periodically throughout the course.
Prerequisite: Students are eligible if they have successfully completed Algebra I.
Geometry Honors

2 Semesters, 1 Credit, Full-Time

A rigorous course covering the topics included in the Geometry course in greater detail. There will also be an introduction into the basic concepts of Probability and Statistics. Problems are more rigorous than in the Geometry course, with an emphasis on proofs and a faster pace. Probability and Statistics topics include: presenting data, analyzing data, normal distributions, correlation, permutations, combinations, probability, mutually exclusive and independent events. In addition, algebra topics are reviewed periodically throughout the course.
Prerequisite: Students are eligible if they have earned an A- or higher in Algebra I.
Intro to Computer Programming I-

.25 credit / meets twice during the rotation

This course is a continuation of Introduction to Computer Programming I. Students will extend their knowledge of Python by writing programs that include strings, lists, arrays, text input and output, searching and sorting, and recursion. Students will also transition to Java programming language in preparation for the AP Computer Science A (Java) course.

Prerequisite: B- or higher in Introduction to Computer Programming I
Intro to Computer Programming II - I.S.

2 semesters / .5 credit / Pass-Fail / Independent Study Only
Introduction to Computer Programming I

2 Semesters, .5 Credit, Part Time Course

Focuses on simple to complex programming solutions of various problems. By using the Python programming language, students will learn to write programs that include if-then decisions, while loops, input and output, functions, and strings, as well as the top-down and modular approach to programming. Programming assignments will relate to a variety of real-life applications.

Prerequisite: Students are eligible if they have successfully completed Algebra I.
Introduction to Computer Programming II (I.S.)

2 Semesters, .5 Credit, Part Time Course (Independent Study Only)

This independent study course is a continuation of Intro. to Computer Programming I. Students will extend their knowledge of Python by writing programs that include strings, lists, arrays, text input and output, searching and sorting, and recursion. Students will also transition to Java programming language in preparation for the AP Computer Science A (Java) course.

Prerequisite: Students are eligible if they have earned a B+ or higher in Introduction to Computer Programming I.
Linear Algebra Honors-S1

1st Semester, .5 Credit, Full Time Course (Gr. 11 and 12)

A modern elementary introduction to linear algebra with an emphasis on techniques and theory. Topics include: matrix operations, properties of determinants, vectors in two and three dimensions, linear transformations, eigenvalues, eigenvectors, dot products and inner spaces.

Prerequisite: Students are eligible if they have earned either a B- or higher in AP Calculus BC and a score of 3 or higher on the AP Calculus BC exam, or a B- or higher in Calculus II Honors.
Multivariable Calculus Honors-S2

2nd Semester, .5 Credit, Full Time Course (Grades 11-12)

A continuation of the foundation of topics developed in AP Calculus BC. Topics will include vector algebra, vector calculus, partial derivatives, gradients and directional derivatives, tangent planes, multiple integrals, and line integrals.
Students in this course are expected to purchase a TI-84 graphing calculator.

Prerequisite: Students are eligible if they have earned either a B- or higher in AP Calculus BC and a score of 3 or higher on the AP Calculus BC exam, or a B- or higher in Calculus II Honors.
Numerical Analysis Honors

2 Semesters, 1 Credit, Full Time Course (Grades 11-12)

The mathematics of solutions to problems that cannot be solved analytically. The course will focus on developing and studying algorithms for solutions to such problems, including linearization analysis, various methods for zeros (bisection, Newton's), and Newton's method for differential equations. Other methods involving infinite series for computing sine and cosine will also be considered. Where appropriate along the way, coding these routines in Python will be implemented, and the results will be compared to known values found with a standard evaluation package.
Prerequisite: Minimum grade of B- in AP Calculus BC with a grade of 3 or more on the AP Calculus BC exam or minimum grade of B- in Calculus II Honors
Numerical Analysis Honors-S2

1 Semesters, 1 Credit, Full Time Course (Grades 11-12)

The mathematics of solutions to problems that cannot be solved analytically. The course will focus on developing and studying algorithms for solutions to such problems, including linearization analysis, various methods for zeros (bisection, Newton's), and Newton's method for differential equations. Other methods involving infinite series for computing sine and cosine will also be considered. Where appropriate along the way, coding these routines in Python will be implemented, and the results will be compared to known values found with a standard evaluation package.
Prerequisite: Minimum grade of B- in AP Calculus BC with a grade of 3 or more on the AP Calculus BC exam or minimum grade of B- in Calculus II Honors
Precalculus

2 Semesters, 1 Credit, Full Time Course

A course designed to prepare students for the study of calculus. Topics include: elementary algebraic functions (polynomial, rational, power) piecewise, logarithmic, exponential, and trigonometric functions, algebraic manipulation skills, and methods for solving equations. Exposure to logarithmic, exponential, and trigonometric functions is at the introductory level. Students in this course are expected to purchase a TI-84 graphing calculator.
Prerequisite: Students are eligible if they have successfully completed Algebra II or Algebra II Honors.
Precalculus Honors

2 Semesters, 1 Credit, Full-time

A fast-paced and intensive course in preparation for AP Calculus (AB or BC). Topics include: the properties and techniques of advanced graphing, solutions of the elementary functions (polynomial, rational power, piecewise, exponential, logarithmic, logistic, and trigonometric), complex numbers, sequences and series, and an introduction to limits. Students in this course are expected to purchase a TI-84 graphing calculator. Prerequisite: Students are eligible if they have earned either a B+ or higher in Algebra II Honors or an A+ in Algebra II.
Probability and Statistics

2 Semesters, 1 Credit, Full Time Course

This course provides students with an opportunity to develop the statistical literacy and critical thinking skills necessary to analyze and interpret data. The various methods used to properly gather, organize, summarize, and graph sets of data are presented. Methods of inferential statistics are utilized to generalize about populations, develop probability distributions, test hypotheses, and determine validity of results.
Prerequisite: Students are eligible if they have successfully completed Algebra II or Algebra II Honors.
Probability and Statistics-S1

2 Semesters, 1 Credit, Full Time Course

This course provides students with an opportunity to develop the statistical literacy and critical thinking skills necessary to analyze and interpret data. The various methods used to properly gather, organize, summarize, and graph sets of data are presented. Methods of inferential statistics are utilized to generalize about populations, develop probability distributions, test hypotheses, and determine validity of results. Prerequisite: Algebra II or Algebra II Honors
ST-Algebra

1 credit / Offered to students entering grades 7, 8 and 9**

An introduction to algebra. Topics include: polynomials in one and two variables, solutions of linear equations and inequalities, linear functions and graphing, systems of two equations in two unknowns, rational algebraic expressions, quadratic equations solved by factoring and the quadratic formula, proportions and percents, irrational numbers, and application problems.

Students in this course are expected to purchase a TI-84 graphing calculator.

**Prerequisites: This is an intense, fast-paced course designed for students who have successfully completed Pre-Algebra. A recommendation from your current math teacher is required.
ST-Geometry

1 credit / Offered to students entering grades 9 and 10**

Euclidean plane geometry is the focus of this course. There will also be an introduction into the basic concepts of Probability and Statistics. Geometric topics include: basic undefined terms, formal and informal definitions, deductive reasoning, parallel lines, congruent triangles, quadrilaterals, similar triangles, right triangles and the Pythagorean theorem, right triangle trigonometry, circles, and areas and volumes of plane and solid figures. Probability and Statistics topics include: presenting data, analyzing data, normal distributions, correlation, permutations, combinations, probability, mutually exclusive and independent events. In addition, algebra topics are reviewed periodically throughout the course.

Students in this course are expected to purchase a TI-84 graphing calculator.

**Prerequisites: This is an intense, fast-paced course designed for students who have successfully completed Algebra I and Algebra II or Algebra I and have a strong teacher recommendation.
ST-Geometry Honors

1 credit / Offered to students entering grades 7, 8, 9 and 10**

Euclidean plane geometry is the focus of this course. There will also be an introduction into the basic concepts of Probability and Statistics. Geometric topics include: basic undefined terms, formal and informal definitions, deductive reasoning, parallel lines, congruent triangles, quadrilaterals, similar triangles, right triangles and the Pythagorean theorem, right triangle trigonometry, circles, and areas and volumes of plane and solid figures. Probability and Statistics topics include: presenting data, analyzing data, normal distributions, correlation, permutations, combinations, probability, mutually exclusive and independent events. In addition, algebra topics are reviewed periodically throughout the course.

Students can take the course for honors by staying for an extra hour. This course is more rigorous, covering the topics included in the Geometry course in greater detail, with an emphasis on proofs and a faster pace.

Students in this course are expected to purchase a TI-84 graphing calculator.

**Prerequisites: Students must have a minimum year-to-date grade of a B+ in Algebra II or a B+ in Algebra I with a strong teacher recommendation.
ST-Introduction to Computer Programming I

0.5 credit / Offered to students entering grades 8, 9, 10, 11 and 12**

This course focuses on simple to complex programming solutions of various problems. By using Python programming language, students will learn to write programs that include if-then decisions, while loops, input and output, functions, and strings, as well as the top-down and modular approach to programming. Programming assignments will relate to a variety of real-life applications. Advanced techniques with arrays and linked lists will be explored and discussed as time permits.

**Prerequisite: Successful completion of or concurrently enrolled in Algebra II.

Fee: $625.00 (does not include course materials)
ST-Precalculus

1 credit / Offered to students entering grades 9, 10, 11 and 12**

A course designed to prepare students for the study of calculus. Topics include: elementary algebraic functions (polynomial, rational, power), piecewise, logarithmic, exponential, and trigonometric functions, algebraic manipulation skills, and methods for solving equations. Exposure to logarithmic, exponential, and trigonometric functions is at the introductory level.

Students in this course are expected to purchase a TI-84 graphing calculator.

**Prerequisites: This is an intense, fast-paced course designed for students who have successfully completed Algebra I, Algebra II, and Geometry or Geometry Honors.
ST-Precalculus Honors

1 credit / Offered to students entering grades 9, 10, 11 and 12**

A course designed to prepare students for the study of calculus. Topics include: elementary algebraic functions (polynomial, rational, power), piecewise, logarithmic, exponential, and trigonometric functions, algebraic manipulation skills, and methods for solving equations. Exposure to logarithmic, exponential, and trigonometric functions is at the introductory level. Students can take the course for honors by staying for an extra hour. Topics include: the properties and techniques of advanced graphing, solutions of the elementary functions (polynomial, rational power, piecewise, exponential, logarithmic, logistic, and trigonometric), complex numbers, sequences and series, and an introduction to limits.

Students in this course are expected to purchase a TI-84 graphing calculator.

**Prerequisites: Students must have a minimum year-to-date grade of a B+ in Geometry Honors or Algebra II Honors.
AP Statistics-S

2nd Semester, .5 Credit

Curriculum for this course follows the AP Statistics curriculum set by the College Board and is designed to prepare students for the AP Statistics exam in May. The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course draws connections between all aspects of the statistical process, including design, analysis, and conclusions. Additionally, using the vocabulary of statistics, this course will teach students how to communicate statistical methods, results and interpretations. Students will learn how to use graphing calculators and read computer output in an effort to enhance the development of statistical understanding.

Students in this course are expected to purchase a TI-84 graphing calculator.
Co-requisite: Precalculus or Precalculus Honors with department approval.
Numerical Analysis A Honors-S1

Numerical Analysis Honors A and B may be taken as a full year sequence or either semester may be taken as a stand-along semester course. This course explores the mathematics of solutions to problems that cannot be solved analytically. It focuses on developing and studying algorithms for solutions to such problems, including finding zeros, finding extrema, interpolation, regression, integration, differentiation, and differential equations, Where appropriate along the way, coding these routines in Python will be implemented, and the results will be compared to known values found with a standard evaluation package.
Prerequisite: Students are eligible if they have earned either a B- or higher in AP calculus BC and a score of 3 or higher on the AP Calculus BC exam, or a B- or higher in Calculus II Honors.
Numerical Analysis B Honors-S2

Numerical Analysis Honors A and B may be taken as a full year sequence or either semester may be taken as a stand-along semester course. This course explores the mathematics of solutions to problems that cannot be solved analytically. It focuses on developing and studying algorithms for solutions to such problems, including finding zeros, finding extrema, interpolation, regression, integration, differentiation, and differential equations, Where appropriate along the way, coding these routines in Python will be implemented, and the results will be compared to known values found with a standard evaluation package.
Prerequisite: Students are eligible if they have earned either a B- or higher in AP calculus BC and a score of 3 or higher on the AP Calculus BC exam, or a B- or higher in Calculus II Honors.
Personal Finance-S1

1st Semester, 0.5 Credit, Full-Time

This semester-long course equips students with the knowledge, skills, and habits of mind needed to make informed and responsible financial decisions. Students study core financial concepts including banking and saving, budgeting, responsible consumer behavior, credit and debt management, taxes, investing, retirement planning, insurance, and postsecondary financial planning. Career readiness is a central focus, with instruction in job searching, resume and cover letter writing, interviewing, and workplace success, while students also develop practical skills to manage risk, avoid fraud and scams, protect their identities, and advocate for their financial well-being. By the end of the course, students are prepared to navigate real-world financial decisions with confidence, ethical awareness, and resilience as they transition to adulthood.
This course fulfills the requirements of Act 25 of 2023. All Upper School students are required to complete Personal Finance in grades 10, 11, or 12, beginning with the Class of 2029. Online self-paced and summer versions of the course are being developed as additional options in future years.
Prerequisite: Students are eligible if they have successfully completed Algebra I.
Personal Finance-S2

2nd Semester, 0.5 Credit, Full-Time

This semester-long course equips students with the knowledge, skills, and habits of mind needed to make informed and responsible financial decisions. Students study core financial concepts including banking and saving, budgeting, responsible consumer behavior, credit and debt management, taxes, investing, retirement planning, insurance, and postsecondary financial planning. Career readiness is a central focus, with instruction in job searching, resume and cover letter writing, interviewing, and workplace success, while students also develop practical skills to manage risk, avoid fraud and scams, protect their identities, and advocate for their financial well-being. By the end of the course, students are prepared to navigate real-world financial decisions with confidence, ethical awareness, and resilience as they transition to adulthood.
This course fulfills the requirements of Act 25 of 2023. All Upper School students are required to complete Personal Finance in grades 10, 11, or 12, beginning with the Class of 2029. Online self-paced and summer versions of the course are being developed as additional options in future years.
Prerequisite: Students are eligible if they have successfully completed Algebra I.
Probability and Statistics-S

1st Semester, .5 Credit

Serves as a one-semester introductory course. Topics include: collecting, interpreting, and presenting data graphically and analytically, introduction to inferential statistics, and elementary probability theory. Students in this course are expected to purchase a TI-84 graphing calculator.

Pre-Requisite: Successful completion of Calculus or higher.
AND

Co-requisite: Pre-calculus or Pre-calculus Honors WITH department approval.

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Mathematics and Computer Science

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