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The Mathematics Department offers a college preparatory program in mathematics for all students, recognizing the range of mathematical abilities and individual differences within the student body. Sound analytical judgment and intellectual development are fostered in the students. Through the use of exploration and discovery, they are encouraged to use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content, to express mathematical ideas orally and in writing, to judge the validity of arguments, to use and value the connections among mathematical topics and between mathematics and other disciplines, to appreciate the power of mathematical abstraction and symbolism, and to model real-world phenomena with a variety of functions. It is expected that they become logical thinkers, confident in their mathematical abilities and responsible for their own learning. The use of technology is integrated throughout the courses as an aid to developing conceptual understanding.

COURSE OFFERINGS

Algebra I - 9th year
The ninth year algebra course introduces the student to the study of the basic concepts and techniques of algebra. All freshmen are enrolled in a section of this course except those who are placed in Algebra II & Geometry Honors based on the algebra placement examination. An accelerated section of this course, intended for those having prior experience with algebra or who qualify on a placement test, allows for the preliminary study of intermediate algebra during the second semester.

Geometry - 10th year
The course in geometry is a comprehensive study of inductive and deductive reasoning as applied to plane and space figures. Skills and techniques are developed that allow the student to apply postulates, axioms, and theorems to theorem proving and proof writing. Algebraic skills are strengthened through applications to practical problem solving.

Algebra II & Geometry Honors - 9th /10th year
Students who have successfully completed the accelerated Algebra I section (or have placed out of it as freshmen) and have obtained the recommendation of the Mathematics Department are enrolled in this course. During the first semester, this course completes the study of intermediate algebra. In the second semester, the geometry curriculum is covered. This accelerated course is designed to permit advanced math students to progress through the curriculum at a faster pace, allowing the study of precalculus the following year.

Algebra II & Trigonometry - 11th year
This intermediate algebra and trigonometry course further develops algebraic skills and extends the student's ability to reason logically. A solid background is provided for the student who wishes to continue on to precalculus.

Precalculus - 10th/11th year; 12th year, Elective
This course is open to sophomores or juniors who have completed Algebra II & Geometry Honors in good standing, and to seniors who wish to take a fourth year of mathematics and have a strong foundation in mathematics, but are in need of further preparation before formal study of calculus.

The theme of the course is the study of elementary functions based on an examination of the properties of number systems. Topics covered include: the principles of mathematical logic; exponential, logarithmic, circular, and trigonometric functions and their properties; sequences and series; mathematical induction; the binomial theorem; complex numbers; and matrices.

Discrete Mathematics - 12th year, Elective
The technological advances of recent years have placed increased importance on certain areas of mathematics. While the impetus to study discrete mathematical concepts has come from the area of computer science, the value of these topics extends to social sciences, engineering and the natural sciences. Students in this course strengthen their mathematical modeling and reasoning skills and their ability to estimate, generalize and simplify. This course covers such topics as: set theory and logic; elementary number theory; combinatories and probability; algorithmic approaches to problem solving; and statistics.

AP Calculus/AB - 11/12th year, Elective
This Advanced Placement course is an introduction to differential and integral calculus including work in analytic geometry. It is offered to students who have successfully completed the precalculus course and have obtained the recommendation of the Mathematics Department. Students take the Calculus/AB Advanced Placement examination at the conclusion of this course. This course is also available for juniors who have completed Precalculus Honors.

AP Calculus/BC - 12th year, Elective
This Advanced Placement course is available to those who complete Calculus/AB during junior year. It is designed to qualify the student for college placement and credit one semester beyond that granted for Calculus/AB. Topics such as vector functions, parametric equations, polar curves, and sequences and series are covered in depth. Students wishing to take this course must obtain the recommendation of the Mathematics Department, and will be expected to take the Calculus/BC Advanced Placement examination at the conclusion of the course.

AP Statistics- 12th year, Elective
This course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data by observing patterns and departures from patterns; planning a study by deciding what and how to measure; anticipating patterns by producing models using probability theory and simulation; and using statistical inference to confirm models.

Computer Laboratory - 9th year (¼ credit)
The Computer Lab class is a series of laboratory sessions designed to help students increase their proficiency in computer skills. Word processing, spreadsheets, and data organization are highlighted, with specific applications to the needs of the Loyola student -- essay and term paper writing for their classes, college essay writing, resume preparation, etc. Students are introduced to the proper use of the Internet for educational purposes. Students are also familiarized with the many programs available for their use in the computer room. These programs include: tutorial programs in various subject areas; SAT preparation programs; college selection programs; and desktop publishing and graphics programs.

Computer Science - 12th year, Elective
The main objective of this course is to gain greater understanding of computers through software applications. This understanding will result in the students' ability to learn real skills that are already a necessity on today's college campuses and in the business world. The first semester focus is on Internet applications and the second semester focus is on database applications. A secondary objective in the course is for students to learn about the computer industry through readings and guest lectures. Students will be encouraged to reflect on technology's impact on society as well.

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