Academic Catalog

Mathematics (MATH)

MATH 1A  •  CALCULUS

MATH 1A Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 48C or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in MATH 1AH.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Introduction to differential calculus, including limits, derivatives and their applications to curve-sketching, families of functions, and optimization.

MATH 1AH  •  HONORS CALCULUS I

MATH 1AH Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 48C or equivalent.
Corequisite: MATH 1AHP.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in MATH 1A.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade Only
Repeatability: Not Repeatable

Introduction to differential calculus, including limits, derivatives and their applications to curve-sketching, families of functions, and optimization. Honors work emphasizes a deeper study of differential calculus via the study of proofs using analytic techniques, real-world problems, and special applied projects.

MATH 1AHP  •  HONORS CALCULUS I SEMINAR

MATH 1AHP Details
Units: 1
Hours: 1 lecture per week (12 total per quarter)
Corequisite: MATH 1AH.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade Only
Repeatability: Not Repeatable

An honors seminar linked to MATH 1AH. In this course, students will explore a multitude of advanced problems from the calculus I honors course, including proofs of limit laws, differentiation rules, and corresponding theorems concerning the behavior of differentiable functions. As the calculus I honors course will require students to submit typed technical solutions to applied problems, this seminar will support students in learning how to use mathematical typesetting software. Best practices for mathematical writing will also be discussed.

MATH 1B  •  CALCULUS

MATH 1B Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1A or 1AH.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in MATH 1BH.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Introduction to integral calculus, including definite and indefinite integrals, the first and second fundamental theorems and their applications to geometry, physics, and the solution of elementary differential equations.

MATH 1BH  •  HONORS CALCULUS II

MATH 1BH Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1A or 1AH.
Corequisite: MATH 1BHP.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in MATH 1B.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade Only
Repeatability: Not Repeatable

Introduction to integral calculus, including Riemann sums, definite, indefinite, and improper integrals, the first and second fundamental theorems of calculus and their applications to geometry, physics, and solutions to elementary differential equations. Honors work emphasizes more in-depth analysis of real-world problems and the theory through proofs using analysis techniques.

MATH 1BHP  •  HONORS CALCULUS II SEMINAR

MATH 1BHP Details
Units: 1
Hours: 1 lecture per week (12 total per quarter)
Corequisite: MATH 1BH.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade Only
Repeatability: Not Repeatable

An honors seminar for MATH 1BH. In this course, students will explore a multitude of advanced problems from the calculus II honors course, including proofs of the fundamental theorems, properties of integrals, integration techniques, and various other theorems and propositions concerning the behavior of integrable functions. As the calculus II honors course will require students to submit typed technical solutions to applied problems, this lab will support students in learning how to use mathematical typesetting software. Best practices for mathematical writing will also be discussed.

MATH 1C  •  CALCULUS

MATH 1C Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1B or 1BH.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Introduction to functions of more than one variable, including vectors, partial differentiation, the gradient, contour diagrams and optimization. Additional topics include infinite series, convergence and Taylor series.

MATH 1D  •  CALCULUS

MATH 1D Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1C.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Introduction to integration of functions of more than one variable, including double, triple, flux and line integrals. Additional topics include polar, cylindrical and spherical coordinates, parameterization, vector fields, path-independence, divergence and curl.

MATH 2A  •  DIFFERENTIAL EQUATIONS

MATH 2A Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1C.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in MATH 12A.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Differential equations and selected topics of mathematical analysis.

MATH 2B  •  LINEAR ALGEBRA

MATH 2B Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 1C.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

A first course in Linear Algebra, including systems of linear equations, matrices, linear transformations, determinants, abstract vector spaces and subspaces, eigenvalues and eigenvectors, inner product spaces and orthogonality, and selected applications of these topics.

MATH 10  •  ELEMENTARY STATISTICS

MATH 10 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 105 or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; UC will grant transfer credit for a maximum of one course from the following: PSYC 7, SOC 7, MATH 10 or 17--students are strongly encouraged to meet with a counselor for appropriate course selection.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

An introduction to modern methods of descriptive statistics, including collection and presentation of data; measures of central tendency and dispersion; probability; sampling distributions; hypothesis testing and statistical inference; linear regression and correlation; analysis of variance; use of microcomputers for statistical calculations. Illustrations taken from the fields of business, economics, medicine, engineering, education, psychology, sociology, social sciences, life science, and health science.

MATH 12  •  CALCULUS FOR BUSINESS & ECONOMICS

MATH 12 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 48A or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

A study of the techniques of differential and integral calculus, with an emphasis on the application of these techniques to problems in business and economics.

MATH 17  •  INTEGRATED STATISTICS II

MATH 17 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 217.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; UC will grant transfer credit for a maximum of one course from the following: PSYC 7, SOC 7, MATH 10 or 17--students are strongly encouraged to meet with a counselor for appropriate course selection; not open to students with credit in MATH 57.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

The second of two in the Statway sequence. Covers concepts and methods of statistics with an emphasis on data analysis. Topics include methods for collecting data, graphical and numerical descriptive statistics, correlation, simple linear regression, basic concepts of probability, confidence intervals and hypothesis tests for means and proportions, chi-squared tests, and ANOVA. Application problems will be taken from the fields of business, economics, medicine, engineering, education, psychology, sociology and from culturally diverse situations. This sequence is recommended for students with majors that require no mathematics beyond freshman-level statistics.

MATH 22  •  DISCRETE MATHEMATICS

MATH 22 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: C S 1A; MATH 48C or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; not open to students with credit in CIS 18 or C S 18.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable
Cross-Listed: C S 18

Discrete mathematics: set theory, logic, Boolean algebra, methods of proof, mathematical induction, number theory, discrete probability, combinatorics, functions, relations, recursion, algorithm efficiencies, graphs, trees.

MATH 42  •  MATH FOR ELEMENTARY SCHOOL TEACHERS

MATH 42 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 105 or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real numbers systems and subsystems. Emphasis is on comprehension and analysis of mathematical concepts and applications of logical reasoning.

MATH 44  •  MATH FOR THE LIBERAL ARTS

MATH 44 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 105 or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

A survey of mathematical models and other tools to introduce the nonspecialist to the methods of quantitative reasoning. Problem solving by Polya's method with analytic, numeric, graphical, and verbal investigation. Selecting, constructing, and using mathematical models. Interpreting quantitative results in qualitative context. Emphasis on deductive reasoning and formal logic; algebraic, exponential, logarithmic, and trigonometric models; probability and the normal distribution; data analysis; and selected topics from discrete math, finite math, and statistics.

MATH 48A  •  PRECALCULUS I

MATH 48A Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 105 or equivalent.
Corequisite: For students who do not meet the prerequisite requirement, concurrent enrollment in MATH 248A is required.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; UC credit for MATH 48A, 48B and 48C is limited to a maximum of 7.5 units for the combination or any portion of the series completed.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Introduction to functions and families of functions, including linear functions, quadratics, power and radical functions, absolute value functions, piece-wise defined functions, transformations of these functions, composition of these functions and their use in solving application problems.

MATH 48B  •  PRECALCULUS II

MATH 48B Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 48A or equivalent.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; UC credit for MATH 48A, 48B and 48C is limited to a maximum of 7.5 units for the combination or any portion of the series completed.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

This course is a continuation of topics from MATH 48A. Topics include polynomial, rational, exponential and logarithmic functions, transformations of these functions and their use in solving application problems.

MATH 48C  •  PRECALCULUS III

MATH 48C Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Prerequisite: MATH 48B.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249; UC credit for MATH 48A, 48B and 48C is limited to a maximum of 7.5 units for the combination or any portion of the series completed.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Area V: Communication & Analytical Thinking
Transferable: CSU/UC
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

This course is a continuation of topics from MATH 48B. Topics include the six trigonometric functions, trigonometric identities, inverse trigonometric functions, trigonometric equations, right triangles, oblique triangles, vectors, parametric equations, and applications with various functions.

MATH 67  •  ENHANCED MATHEMATICS LEARNING WITH MATHEMATICA

MATH 67 Details
Units: 3
Hours: 3 lecture per week (36 total per quarter)
Advisory: MATH 48A or equivalent; ability to download software and work with basic programs like Word or Excel.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

An introduction to Mathematica mathematics software and its use as a tool for computation and visualization in mathematics and statistics. Use of Mathematica for solving problems taken from algebra and statistics through linear algebra and differential equations. Access to Mathematica provided at no additional cost.

MATH 70R  •  INDEPENDENT STUDY IN MATHEMATICS

MATH 70R Details
Units: 1
Hours: 3 laboratory per week (36 total per quarter)
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Provides an opportunity for the student to expand their studies in Mathematics beyond the classroom by completing a project or an assignment arranged by agreement between the student and instructor. The student is required to contract with the instructor to determine the scope of assignment and the unit value assigned for successful completion. Students may take a maximum of 6 units of Independent Study per department.

MATH 71R  •  INDEPENDENT STUDY IN MATHEMATICS

MATH 71R Details
Units: 2
Hours: 6 laboratory per week (72 total per quarter)
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Provides an opportunity for the student to expand their studies in Mathematics beyond the classroom by completing a project or an assignment arranged by agreement between the student and instructor. The student is required to contract with the instructor to determine the scope of assignment and the unit value assigned for successful completion. Students may take a maximum of 6 units of Independent Study per department.

MATH 72R  •  INDEPENDENT STUDY IN MATHEMATICS

MATH 72R Details
Units: 3
Hours: 9 laboratory per week (108 total per quarter)
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Provides an opportunity for the student to expand their studies in Mathematics beyond the classroom by completing a project or an assignment arranged by agreement between the student and instructor. The student is required to contract with the instructor to determine the scope of assignment and the unit value assigned for successful completion. Students may take a maximum of 6 units of Independent Study per department.

MATH 73R  •  INDEPENDENT STUDY IN MATHEMATICS

MATH 73R Details
Units: 4
Hours: 12 laboratory per week (144 total per quarter)
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: CSU
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Provides an opportunity for the student to expand their studies in Mathematics beyond the classroom by completing a project or an assignment arranged by agreement between the student and instructor. The student is required to contract with the instructor to determine the scope of assignment and the unit value assigned for successful completion. Students may take a maximum of 6 units of Independent Study per department.

MATH 105  •  INTERMEDIATE ALGEBRA

MATH 105 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Advisory: Not open to students with credit in MATH 108.
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: None
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

Quadratic, polynomial, rational, radical, exponential and logarithmic functions and expressions with an emphasis on graphing and applications.

MATH 180  •  QUANTITATIVE REASONING

MATH 180 Details
Units: 5
Hours: 4 lecture, 3 laboratory per week (84 total per quarter)
Degree and Credit Status: Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: None
Grade Type: Letter Grade Only
Repeatability: Not Repeatable

Students will be able to apply mathematical reasoning in their personal, professional, and academic lives, to investigate new contexts, develop and propose possible solutions, discuss and analyze proposed plans, and make decisions. Students will learn to value the collaborative process of explaining, investigating, comparing and assessing a variety of perspectives and approaches. Through immersion in contextualized lessons, students will practice quantitative thinking as they build skill in communication, critical and creative thinking, and computation. They will grow their knowledge and understanding of themselves, each other, and the world through the study of culturally relevant contexts, such as personal finance, health and wellness, membership in society, and the environment.

MATH 217  •  INTEGRATED STATISTICS I

MATH 217 Details
Units: 5
Hours: 5 lecture per week (60 total per quarter)
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Non-Degree-Applicable Credit Course
Basic Skills, 2 Levels Below Transfer
Foothill GE: Non-GE
Transferable: None
Grade Type: Letter Grade (Request for Pass/No Pass)
Repeatability: Not Repeatable

The first of two courses in the Statway sequence. Covers concepts and methods of statistics with an emphasis on data analysis. Topics include methods for collecting data, graphical and numerical descriptive statistics, correlation, simple linear regression, basic concepts of probability, confidence intervals and hypothesis tests for means and proportions, chi-square tests, and ANOVA. Application problems will be taken from the fields of business, economics, medicine, engineering, education, psychology, sociology and from culturally diverse situations. This sequence is recommended for students with majors that require no mathematics beyond freshman-level statistics.

MATH 248A  •  JUST-IN-TIME SUPPORT FOR MATH 48A

MATH 248A Details
Units: 2.5
Hours: 2.5 lecture per week (30 total per quarter)
Corequisite: MATH 48A.
Advisory: Demonstrated proficiency in English by placement via multiple measures OR through an equivalent placement process OR completion of ESLL 125 & ESLL 249.
Degree and Credit Status: Non-Degree-Applicable Credit Course
Foothill GE: Non-GE
Transferable: None
Grade Type: Pass/No Pass Only
Repeatability: Not Repeatable

A just-in-time approach to the core prerequisite skills, competencies, and concepts needed in Precalculus I. Intended for students majoring in science, technology, engineering, and mathematics who are concurrently enrolled in MATH 48A at Foothill College. Topics include: a review of computational skills developed in beginning and intermediate algebra, including factoring, graphing linear equations, solving absolute value equations and inequalities, analyzing functions, including quadratic functions.