This course is designed for the student who is interested in pursuing a college major with a strong emphasis in mathematics. In the first part of the course, the elementary properties of functions and their inverses are reviewed, as well as specific types of functions (exponential, logarithmic, trigonometric). Subsequently, the student is introduced to the concepts of limits and continuity; differentiation and its applications to problems of extrema and related rates of change; anti-differentiation and its application to the solution of differential equations; definite integrals and their application to finding areas, volumes, and length of curves. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
AP Calculus AB
This course is designed for the student who is interested in pursuing a college major with a strong emphasis in mathematics. The course will cover three main topics of Calculus: limits, derivatives, and integrals. The course will emphasize a multi-representational approach to calculus with concepts and solutions expressed graphically, numerically, and analytically. The course emphasizes conceptual understanding of derivatives, integrals, and limits, as well as applications of these concepts. In order to develop these concepts, functions and graphs are a fundamental part of this course. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Mathematics Teaching Assistant
Math Teaching Assistants provide support for the math department (1 hour/week) either before school, after school, or during resource period in one or more of the following ways:
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- Assist students taking courses in which the Teaching Assistant has demonstrated mastery.
- Assist with grading assignments that require no teacher interpretation.
Students interested in being a Teaching Assistant are required to fill out a short application available from their teacher or the math department chair. Teaching Assistants are typically supervised by an individual teacher, whose signature is required at the time of application. Students will be selected based on department needs and student qualifications. In some cases, students taking AP math courses will have priority in being a Teaching Assistant due to their qualifications in offering peer assistance.
Introduction to Finance
Students taking this elective will develop the skills needed to make sound financial decisions. Topics will include planning your career, payroll and taxes, banking, credit, budgeting, purchasing, basic economics, an introduction to stats and business ethics. All of these topics will be taught through a lens of fiscal and ethical responsibility. This course also extends beyond personal finance to some topics more relevant to college level business and finance courses. Therefore, it can provide a stronger foundation for students considering that path of study in college.
AP Statistics
This course is designed to give students a foundation for further studies in math while emphasizing preparation for majors in psychology, sociology, and other non-calculus fields. The course is intended for students wishing to complete the equivalent of a one-semester non-calculus based college course in statistics and will introduce them to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
Math Analysis
This course is designed to give each student thorough preparation in basic Trigonometry and Statistics. THIS COURSE IS NOT MEANT TO BE A PREPARATION FOR CALCULUS. Topics include the Trigonometric and Circular functions and their applications, Identities, Oblique Triangle Trig, and Vectors (in two dimensions) in rectangular and polar form. The course also includes an introduction to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
Honors Linear Algebra Multivariable Calculus
This course covers differential, integral, and vector calculus for functions or more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics. The course opens with a unit on vectors, which introduces students to this critical component of advanced calculus and will culminate in Green’s Stokes’ and Gauss’ Theorems. We will study partial derivatives, double and triple integrals, and vector calculus in both two and three dimensions. Students are expected to develop fluency with vector and matrix operations. Understanding of parametric curves as a trajectory described by a position vector is an essential concept, and this allows us to break free from one-dimensional calculus and investigate paths, velocities, and other applications of science that exist in three-dimensional space. We study derivatives in multiple dimensions, we use the ideas of the gradient and partial derivatives to explore optimization problems with multiple variables, and we consider constrained optimization problems using Lagrangians. After our study of differentials in multiple dimensions, we move to integral calculus. We use line and surface integrals to calculate physical quantities especially relevant to mechanics and electricity and magnetism, such as work and flux, and we employ volume integrals for calculations of mass and moments of inertia.
The study of systems of linear equations, the algebra of matrices, determinants, vector spaces, linear transformations, the algebra of linear transformations with an introduction to dual spaces, eigenvalues and eigenvectors, and the applications of vectors and matrices to linear equations and linear transformations.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations (UC/CSU Subject C Approval Pending)
AP Calculus BC
AP Calculus BC is an extension of AP Calculus AB rather than an enhancement. This course includes all topics covered in the AP Calculus AB course, with similar emphases and similar depth of understanding required. The course also presents intensive study of parametric, polar, and vector functions; sequences and series; and elementary differential equations. A Texas Instruments TI-83 or TI-84 series graphing calculator is required.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations
AP Computer Science A – Java
AP Computer Science A (AP CS-A) is equivalent to a one-semester, introductory college-level computer programming course. AP CS-A 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.
*Class receives honors weighting in SI weighted GPA and UC/CSU GPA calculations.
**Students are required to take the AP Computer Science exam administered in May.
Mathematics
INTRODUCTION — In keeping with the Jesuit tradition of education at St. Ignatius College Preparatory and in accordance with our school’s statement of philosophy, the mission of the Mathematics Department is to develop “men and women for and with others” through a comprehensive and structured mathematics program. We strive to prepare 90% or more of the student body, over the course of four years, for success in a college calculus and/or statistics course. We instill a fundamental appreciation of the techniques of algebra in solution of problems and of logic through the study of geometry. Though only three years of math are required for graduation, we encourage students to continue math through their senior year in order to have the greatest flexibility in choosing courses of study in college.
CRITERIA FOR HONORS ENROLLMENT — Qualifications for honors, accelerated and AP courses includes analysis of the student’s grade in his/her current math course, an evaluation by the current and previous teachers (if applicable) of the student’s grasp and application of concepts, participation, written work, motivation and interest in advanced mathematics study, overall recommendation, and various standardized tests (HSPT and PSAT). In addition, certain grade minimums must be met in order to be considered for an honors or AP course. Final enrollment in an honors or AP course is always contingent upon successful completion of current coursework, even if a student is provisionally admitted to an honors or AP course in the spring.