Upper School Courses

Upper School Mathematics & Computer Science

Students in the Upper School are required to complete three mathematics credits and take math through their junior year. Students may earn six credits in mathematics at St. Stephen’s by taking Algebra I in the Middle School or by presenting credits at entrance and demonstrating performance capability. Advanced sections above Algebra I cover the subject in greater depth and breadth and are so designated on students’ transcripts.  Admission to and retention in an advanced course is by departmental approval and may require confirmation of ability by a placement examination.

List of 17 items.

  • Algebra I

    Algebra I integrates knowledge of variables and their use with concepts and operations of arithmetic in a formal, logical development of elementary algebra. Accuracy and precision are essential components of instruction, as is the development of problem-solving strategies. The content of the course includes an in-depth study of linear equations and inequalities, graphing, operations with polynomials, factoring, rational expressions and equations, introduction to functions, radical expressions and equations, and the quadratic formula. Word problems and applications of increasing complexity are addressed throughout the course.
  • Geometry

    Students are introduced to traditional plane and solid Euclidean geometry as well as coordinate geometry, constructions, and transformational geometry. Both independent problem solving and cooperative group work are elements used in the investigation of geometric truths. Students learn theory and application, formal and informal proofs, and symbolic and visual approaches to problems. The course provides a firm foundation in understanding the relationships between and within geometric figures, and it develops the skills to reason effectively. Computer-assisted explorations, as well as compass and straightedge constructions, are part of the course throughout the year as they relate to the topics covered. The course helps to prepare students for the challenges of higher-level mathematics. Prerequisite: Algebra I
  • Advanced Geometry

    Advanced Geometry is intended for those students who have well-developed spatial and abstract reasoning skills. In addition to the topics presented in Geometry, this course includes a more formal emphasis on deductive logic and proof. Proofs using deductive or indirect reasoning, paragraph or two column form, and construction are utilized to enhance logical thinking and creative problem solving. Inductive discovery of principles is facilitated by the use of the computer, models, and experimentation. Special projects heighten the student’s appreciation for the application of geometry to the real world, the historical significance of the subject, and recent discoveries in mathematics. Prerequisite: V- in Advanced Algebra I or departmental approval
  • Algebra II

    Algebra II builds on the concepts and skills mastered in Algebra I and expands these ideas with further applications and more challenging problem solving. It also utilizes technology, primarily in the form of graphing calculators, as a tool for opening doors to new approaches. In addition to the topics introduced in Algebra I, Algebra II includes the study of irrational and complex numbers, polynomial equations, exponential and logarithmic functions, analytic geometry, trigonometry, and probability. The course provides a firm foundation in the language and application of algebra and in the skills and knowledge necessary to succeed in higher levels of mathematics. Prerequisite: Geometry
  • Advanced Algebra II

    A rigorous course that prepares students for successful transition into Advanced Precalculus, Advanced Algebra II enables them to master advanced algebraic concepts and skills, to think independently, and to utilize appropriate methods of problem solving. The content of the course includes topics covered in Algebra II as well as combinatorics, probability, and a more in-depth study of trigonometry. Those topics that are covered in Algebra II are studied in greater depth and scope, with special emphasis on critical thinking and application of concepts. Prerequisite: V- in Advanced Geometry or department approval.
  • Precalculus

    Precalculus provides students with a firm foundation in the theory and use of functions and their graphs. Each type of function addressed – including polynomial, rational, exponential, logarithmic, and trigonometric – is explored algebraically, graphically, and geometrically. Other topics include analytic geometry, complex numbers, probability, and sequences and series. Graphing calculators and graphing software are used extensively to enable students to make subtle connections between topics within the course. Prerequisite: G- in Algebra II or departmental approval
  • Advanced Precalculus

    Advanced Precalculus is a more rigorous examination of those topics essential to the study of calculus. Major topics include the study of advanced graphing, functional analysis, exponential and logarithmic functions, trigonometric functions and their applications, analytic geometry, sequences and series, combinatorics and probability, matrices, polar and parametric functions, and polar representation of complex numbers. An introduction to calculus at the end of the course includes limits, continuity, and the development of instantaneous rates of change.   Emphasis is on conceptual understanding and real world applications. Prerequisite: V- in Advanced Algebra II or departmental approval
  • Calculus

    This course is designed to prepare students for a college level calculus course, with an emphasis on process and applications rather than on theory. The topics include a Precalculus review, functions and their graphs, limits, derivatives and applications, integration, and the calculus of exponential, logarithmic and trigonometric functions. Prerequisite: G- in Precalculus or departmental approval
  • Advanced Calculus AB

    Advanced Calculus AB is a standard college level course in the calculus of one variable. Emphasis is not only on a clear understanding of the concepts, but also on their applicability in real world situations. Major topics include limits, continuity, derivatives and applications, integrals and applications, transcendental functions, and first order differential equations. Mastery and retention of Advanced Precalculus topics are assumed.  Prerequisite: V- in Advanced Precalculus or departmental approval
  • Advanced Calculus BC

    Advanced Calculus BC is a rigorous, in-depth study of the calculus of one variable.  In addition to the topics presented in the Advanced Calculus AB course, this course includes topics such as infinite series, Taylor polynomials, parametrically defined functions, and polar coordinates. Mastery and retention of Advanced Precalculus topics are assumed. Prerequisite: departmental approval
  • Multivariable Analysis

    Students are introduced to further mathematical applications of calculus, as well as other topics in advanced mathematics. Topics include: advanced techniques of integration; three-dimensional analytic geometry; vectors and vector-valued functions; multivariable and vector calculus, including multiple and line integrals; and the theorems of Green and Stokes. Prerequisite: departmental approval
  • Statistics and Selected Topics in Mathematics

    This course offers students an alternative in the mathematics they choose to pursue beyond the level of second year algebra. Approximately half the year is spent introducing students to the core concepts of statistics; in the other half, students explore the applications of mathematics in diverse contexts, including career and daily life. Throughout the course, students focus on the mathematical techniques of problem solving and analysis that foster habits of effective thinking in life outside the classroom. Topics may include some or all of the following: networks, graphs, and critical paths; fractal geometry; non-Euclidean geometry; topology; logic, binary arithmetic, digital logic, encoding and the mathematics of computers; number theory; personal finance and avenues of investment. Prerequisite: Algebra II
  • Advanced Statistics

    This activity-based course provides students with a rigorous, in-depth study of the fundamental concepts and techniques employed when working with data. The course exposes students to four broad conceptual themes: exploratory analysis, planning a study, modeling using probability and simulation, and testing hypotheses using statistical inference. Technology plays a major role in the course. Statistical computer software is used, and students learn to use the Internet as part of the statistical research process. Motivated students who have completed Algebra II should consider taking Statistics as an alternative or supplement to Precalculus and/or Calculus. Prerequisite: Algebra II. Preference will be given to Seniors enrolling in this course.
  • Computer Science

    Students are introduced to computer programming and Object-Oriented design methods. Students learn to use a variety of resources and approaches to write, test, and correct programs. Individual and group assignments allow the student to develop both theoretical and hands-on programming skills. Previous experience in computer programming is not required. Prerequisite: Geometry
  • Advanced Computer Science

    Students continue the study of computer science topics, including advanced algorithms, advanced data structures, and formal efficiency analysis.  Students will study object-oriented design topics (including data encapsulation, inheritance, and polymorphism). Students will use program specifications to develop test cases, design programs, and implement those designs in Java.  Prerequisite: V- in Computer Science or department approval
  • App Development

    Students will learn to design and develop mobile apps for multiple platforms, starting with Bubble web platform and moving to Xamarin in Visual Studio using C#. Students will be expected to consider development, design, and entrepreneurship when working collaboratively to create their app. Throughout the year, students will use design thinking to create human-centered app solutions that meet a need in their communities.
    Prerequisites: Algebra I is preferred but not required. Students should be self-driven and comfortable with project-based learning.
  • Independent Study in Advanced Mathematics

    Students who have completed Multivariable Analysis before the senior year may work with a faculty member to complete a course of study in advanced topics such as differential equations, linear algebra, abstract algebra, or topology. Prerequisite: departmental approval
Address: 6500 St. Stephen's Dr., Austin, TX 78746
Phone: (512) 327-1213