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- Courses - Mathematics

# Mathematics

Mathematics is one of the oldest intellectual disciplines, yet it has never lost its relevance; we are continually finding new and exciting applications in fields as diverse as biology and counter-terrorism. Mathematical methods play a pivotal role in bioinformatics, cryptography, computer graphics, analysis of large-scale networks, cyber security and operations research, as well as in computer science, engineering, business, and the natural, physical and social sciences. Applications of mathematics can be found in many vocational disciplines such as carpentry, electronics, automotive technology and welding. The Mathematics department at Las Positas College offers a wide range of courses in a variety of formats designed to meet the needs of a diverse student population. Whatever your educational goals, we have the courses you need to succeed. We offer a full lower-division curriculum which prepares students for transfer to four-year institutions, as well as basic skills and associate degree applicable courses.

## Degrees:

## Career Opportunities

The Associate of Science Degree in Mathematics for Transfer is intended to provide an option for students who plan to complete a bachelor’s degree in a similar major at a CSU campus, or pursue a teaching career, since teachers of mathematics are always in demand. The study of mathematics can prepare students for a variety of technical and scientific careers. The problem-solving and communication skills acquired are valuable in business, industry, and everyday life, and mathematics is an essential component of any engineering or science degree.

## Mathematics Courses

### MATH 1 - Calculus I

**5 units**

An introduction to single-variable differential and integral calculus including: functions,
limits and continuity; techniques and applications of differentiation and integration;
the Fundamental Theorem of Calculus; areas and volumes of solids of revolution. Prerequisite:
MATH 30 with a minimum grade of C, MATH 39 with a minimum grade of C. 90 hours lecture.
AA/AS GE. Transfer: CSU, UC*; CSU GE: B4; IGETC: 2A; C-ID# MATH 211, MATH 900 S (if
taken with MATH 2). ** MATH 1, 33, and 34 combined: maximum UC credit, one course.*

- Degree Applicable, Credit
- Grading Option: GR

### MATH 2 - Calculus II

**5 units**

Continuation of single-variable differential and integral calculus. Topics covered include: inverse and hyperbolic functions; techniques of integration; polar and parametric equations; infinite sequences, series, power series and Taylor series; applications of integration. Primarily for mathematics, physical science and engineering majors. Prerequisite: MATH 1 with a minimum grade of C. 90 hours lecture. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# MATH 221, MATH 900 S (if taken with MATH 1).

- Degree Applicable, Credit
- Grading Option: GR

### MATH 3 - Multivariable Calculus

**5 units**

Vector valued functions, functions of several variables, partial differentiation, multiple integration, change of variables theorem, scalar and vector fields, gradient, divergence, curl, line integral, surface integral, Green’s Stokes’ and divergence theorem, applications. Prerequisite: MATH 2 with a minimum grade of C. 90 hours lecture. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# MATH 230.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 5 - Ordinary Differential Equations

**3.5 units**

Introduction to differential equations including the conditions under which a unique solution exists, techniques for obtaining solutions, and applications. Techniques include generation of series solutions, use of Laplace Transforms, and the use of eigenvalues to solve linear systems. Generation of exact solutions, approximate solutions, and graphs of solutions using MATLAB. Prerequisite: MATH 3 with a minimum grade of C. 54 hours lecture, 27 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# MATH 240.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 7 - Elementary linear Algebra

**3.5 units**

An introduction to linear algebra including: techniques and theory needed to solve and classify systems of linear equations using Gaussian elimination and matrix algebra; properties of vectors in n-dimensions; generalized vector spaces, inner product spaces, basis, norms, orthogonality; eigenvalues, eigenspaces; and linear transformations. Selected applications of linear algebra, including the use of MATLAB™ to solve problems involving advanced numerical computation. Prerequisite: MATH 2 with a minimum grade of C. 54 hours lecture. 27 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# MATH 250.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 10 - Discrete Mathematical Structures

**4 units**

Designed for majors in mathematics and computer science, this course provides an introduction to discrete mathematical structures used in Computer Science and their applications. Course content includes: Propositional and predicate logic; rules of inference; quantifiers; elements of integer number theory; set theory; methods of proof; induction; combinatorics and discrete probability; functions and relations; recursive definitions and recurrence relations; elements of graph theory and trees. Applications include: analysis of algorithms, Boolean algebras and digital logic circuits. Students who have completed, or are enrolled in, CS 17 may not receive credit. Prerequisite: MATH 1 with a minimum grade of C (May be taken concurrently), CS 1 with a minimum grade of C (May be taken concurrently). 72 hours lecture, 18 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# COMP 152.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 27 - Number Systems for Educators

**3 units**

This course focuses on the development of quantitative reasoning skills through in-depth, integrated explorations of topics in mathematics, including real number systems and subsystems. Emphasis is on comprehension and analysis of mathematical concepts and applications of logical reasoning. Prerequisite: MATH 50 with a minimum grade of C or MATH 55 with a minimum grade of C or NMAT 255 with a minimum grade of C or NMAT 250 with a minimum grade of C. 54 hours lecture. AA/AS GE. Transfer: CSU, UC

- Degree Applicable, Credit
- Grading Option: GR

### MATH 29 - Independent Study, Mathematics

**0.5 - 2 units**

For course information, see "Independent Studies". 27-108 hours laboratory.

### MATH 30 - College Algebra for STEM

**4 units**

College algebra core concepts relating to Science, Technology, Engineering and Mathematics (STEM) and Business fields are explored, such as: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; and analytic geometry. Multiple representations, applications and modeling with functions are emphasized throughout. May not receive credit if Mathematics 20 or 45 have been completed. Prerequisite: MATH 55 with a minimum grade of C or MATH 55B with a minimum grade of C or NMAT 255 with a minimum grade of C. 72 hours lecture, 18 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4, IGETC: 2A; C-ID# MATH 151.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 33 - Finite Mathematics

**4 units**

Linear functions, systems of linear equations and inequalities, exponential and logarithmic
functions and applications, matrices, linear programming, mathematics of finance,
sets and Venn diagrams, combinatorial techniques and an introduction to probability.
Applications in business, economics and social sciences. Prerequisite: MATH 50 with
a minimum grade of C or MATH 55 with a minimum grade of C or MATH 55B with a minimum
grade of C or NMAT 250 with a minimum grade of C or NMAT 255 with a minimum grade
of C. 72 hours lecture. AA/AS GE. Transfer: CSU, UC*; CSU GE: B4; IGETC: 2A; C-ID#
MATH 130. ** MATH 1, 33, and 34 combined: maximum UC credit, one course.*

- Degree Applicable, Credit
- Grading Option: GR

### MATH 34 - Calculus for Business and Social Sciences

**5 units**

Functions and their graphs; limits of functions; differential and integral calculus
of algebraic, exponential and logarithmic functions. Applications in business, economics,
and social sciences and use of graphing calculators. Partial derivatives and the method
of LaGrange multipliers. Prerequisite: MATH 55 with a minimum grade of C or MATH 55B
with a minimum grade of C or NMAT 255 with a minimum grade of C. 90 hours lecture.
AA/AS GE. Transfer: CSU, UC*; CSU GE: B4; IGETC: 2A; C-ID# MATH 140. ** MATH 1, 33, and 34 combined: maximum UC credit, one course.*

- Degree Applicable, Credit
- Grading Option: GR

### MATH 39 - Trigonometry

**4 units**

Trigonometry includes definitions of the trigonometric functions and their inverses, graphs of the trigonometric functions and their inverses, trigonometric equations, trigonometric expressions and identities, including proofs, an introduction to vectors, polar coordinates and complex numbers. Applications include solving right triangles and solving triangles using the law of sines and the law of cosines. Prerequisite: MATH 55B with a minimum grade of C or MATH 55 with a minimum grade of C or NMAT 255 with a minimum grade of C. 72 hours lecture, 18 hours laboratory. AA/AS GE. Transfer: CSU; CSU GE: B4; C-ID# MATH 851.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 40 - Statistics and Probability

**4 units**

Descriptive statistics, including measures of central tendency, dispersion and position; elements of probability; confidence intervals; hypothesis tests; two-population comparisons; correlation and regression; goodness of fit; analysis of variance; applications in various fields. Introduction to the use of a computer software package to complete both descriptive and inferential statistics problems. Prerequisite: MATH 55 with a minimum grade of C or MATH 55B with a minimum grade of C or MATH 50 with a minimum grade of C or NMAT 250 with a minimum grade of C or NMAT 255 with a minimum grade of C. 72 hours lecture, 18 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A; C-ID# MATH 110.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 47 - Mathematics for Liberal Arts

**3 units**

An introduction to a variety of mathematical concepts for students interested in liberal arts. Intended to cultivate an appreciation of the significance of mathematics in daily life and help develop students' mathematical reasoning. Topics include personal finance, logic, and exponential growth. Prerequisite: MATH 55 with a minimum grade of C or MATH 55B with a minimum grade of C or MATH 50 with a minimum grade of C or NMAT 250 with a minimum grade of C or NMAT 255 with a minimum grade of C. 54 hours lecture, 18 hours laboratory. AA/AS GE. Transfer: CSU, UC; CSU GE: B4; IGETC: 2A.

- Degree Applicable, Credit
- Grading Option: GR

### MATH 50 - Intermediate Algebra for SLAM

**4 units**

This is an Intermediate Algebra course for students interested in fields of study that require Statistics or Liberal Arts Mathematics (SLAM). Intermediate algebra concepts will be explored in the context of the function. Function concepts covered include: distinction between functions and relations, domain and range, function notation, multiple representation of functions, behavior of functions, operations with functions (including composition), one-to-one functions, and invertible functions. Types of functions considered: polynomial, rational, radical, exponential and logarithmic functions. The course includes an introduction to probability, counting and quantitative data. Standards for mathematical practice, applications of functions, and modeling with functions are emphasized throughout. Strongly Recommended: MATH 110 with a minimum grade of C or MATH 110B with a minimum grade of C or NMAT 210 with a minimum grade of C. 54 hours lecture, 54 hours laboratory. AA/AS GE.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 52A - Technical Intermediate Algebra for Automotive Technology A

**1.5 units**

This course provides a survey of algebraic processes with an emphasis on applications in the automotive trades. Topics covered include, but are not limited to: algebraic expressions; quadratic functions; and functions. This course may not be used as a prerequisite for any transfer level course. Prerequisite: MATH 72D with a minimum grade of C. 27 hours lecture. AA/AS GE.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 52B - Technical Intermediate Algebra for Automotive Technology B

**1.5 units**

This course provides a survey of algebraic and geometric processes with an emphasis on applications in the automotive trades. Topics covered include, but are not limited to: plane geometry; linear regression, financial mathematics, and measures of central tendency. This course is not intended as a prerequisite for any transfer level course. Prerequisite: MATH 52A with a minimum grade of C. 27 hours lecture. AA/AS GE.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 53A - Technical Intermediate Algebra for Welding A

**2 units**

This course provides a survey of algebraic processes with an emphasis on applications in welding. Topics covered include, but are not limited to: algebraic expressions, plane geometry, the geometry of solids, and triangle trigonometry. This course may not be used as a prerequisite for any transfer level course. Prerequisite: MATH 72C with a minimum grade of C or MATH 72D with a minimum grade of C. 36 hours lecture. AA/AS GE.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 53B - Technical Intermediate Algebra for Welding B

**1 unit**

This course provides a survey of algebraic processes with an emphasis on applications in welding. Topics covered include, but are not limited to: quadratic equations, functions, and mathematical models. This course may not be used as a prerequisite for any transfer level course. Prerequisite: MATH 72D with a minimum grade of C and MATH 53A with a minimum grade of C. 18 hours lecture. AA/AS GE.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 55 - Intermediate Algebra for BSTEM

**5 units**

Intermediate Algebra concepts, in the service of Business, Science, Technology, Engineering and Math fields (BSTEM), will be explored in this course including: an introduction to functions; linear and absolute value functions; absolute value equations and inequalities; compound linear inequalities; rational expressions, functions and equations; radical expressions, functions and equations; rational exponents; complex numbers; quadratic functions and equations; inverse of a function; exponential and logarithmic functions; properties of logarithms; exponential and logarithmic equations; conic sections; and systems of equations and inequalities. Multiple representations, applications and modeling with functions are emphasized throughout. Strongly Recommended: MATH 110 with a minimum grade of C, MATH 110B with a minimum grade of C, or NMAT 210 with a minimum grade of C. 90 hours lecture. AA/AS GE.

- Degree Applicable, Credit.
- Grading Option: OP

### MATH 55C - Concurrent Support for Intermediate Algebra

**1 unit**

This course is concurrent support for Intermediate Algebra. The course is designed to provide additional, formal support to students who are currently taking an Intermediate Algebra. It includes a review of arithmetic, algebraic and geometric concepts that are relevant to their Intermediate Algebra course, study strategies that promote understanding and improve performance, and more indepth investigation of core concepts that are difficult for students to master. Embedded are learning skills such as growth mindset, brain research, time management, study skills, test taking, math anxiety and more. Corequisite: MATH 55 or NMAT 255 or MATH 50 or NMAT 250. 54 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 66 - Math Jam for Calculus I

**0.5 - 1 units**

Math Jam for Calculus I is a credit course for students preparing for Calculus I. Embedded are essential study and life skills to develop each student holistically, including career development. Students will be learning basic skills and transfer-level material with the goal of preparing them to be successful in their upcoming class. It is strongly recommended that students taking this course are enrolled in a calculus course. 27- 54 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 66C - Concurrent Support for Calculus I

**1 unit**

This course offers structured support to students who are concurrently enrolled in Calculus I. The support course includes material to prepare students for the rigor of the calculus course by teaching learning skills necessary to succeed in college courses as well as review of relevant prerequisite algebraic, geometric and trigonometric concepts, and more in-depth investigation of core concepts in their concurrent math course. Corequisite: MATH 1. 54 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 67 - Math Jam for Calculus II

**0.5 units**

Math Jam for Calculus II is a credit course for students preparing for Calculus II. Embedded are essential study and life skills to develop each student holistically, including career development. Students will be learning basic skills and transfer-level material with the goal of preparing them to be successful in their upcoming class. It is strongly recommended that students taking this course are enrolled in a calculus course. 27 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 67C - Concurrent Support for Calculus II

**1 unit**

This course offers structured support to students who are concurrently enrolled in Calculus II. The support course includes material to prepare students for the rigor of the calculus course by teaching learning skills necessary to succeed in college courses as well as review of relevant prerequisite algebraic, geometric and trigonometric concepts, and more in-depth investigation of core concepts in their concurrent math course. Corequisite: MATH 2. 54 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 68 - Math Jam for Calculus III

**0.5 units**

Math Jam for Calculus III is a credit course for students preparing for Calculus III. Embedded are essential study and life skills to develop each student holistically, including career development. Students will be learning basic skills and transfer-level material with the goal of preparing them to be successful in their upcoming class. It is strongly recommended that students taking this course are enrolled in a calculus course. 27 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 68C - Concurrent Support for Calculus III

**1 unit**

This course offers structured support to students who are concurrently enrolled in Calculus III. The support course includes material to prepare students for the rigor of the calculus course by teaching learning skills necessary to succeed in college courses as well as review of relevant prerequisite algebraic, geometric and trigonometric concepts, and more in-depth investigation of core concepts in their concurrent math course. Corequisite: MATH 3. 54 hours laboratory.

- Degree Applicable, Credit
- Grading Option: P/NP

### MATH 72A - Technical Elementary Algebra A

**1 unit**

This course provides a survey of computational and elementary algebraic processes with an emphasis on applications in the automotive and welding trades. Topics covered include, but are not limited to: computations with real numbers, ratios, and proportions. This course cannot be used as a prerequisite for Math 50 Core Intermediate Algebra or Math 55 Intermediate Algebra. 18 hours lecture.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 72B - Technical Elementary Algebra B

**1 unit**

This course provides a survey of computational and elementary algebraic processes with an emphasis on applications in the automotive and welding trades. Topics covered include, but are not limited to: linear equations, the rectangular coordinate system, and linear equations in two variables. This course cannot be used as a prerequisite for Math 50 Core Intermediate Algebra or Math 55 Intermediate Algebra. Prerequisite: MATH 72A with a minimum grade of C. 18 hours lecture.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 72C - Technical Elementary Algebra C

**1 unit**

This course provides a survey of computational and elementary algebraic processes with an emphasis on applications in the automotive and welding trades. Topics covered include, but are not limited to: percentages and measurement. This course cannot be used as a prerequisite for Math 50 Core Intermediate Algebra or Math 55 Intermediate Algebra. Prerequisite: MATH 72A with a minimum grade of C or MATH 72B with a minimum grade of C. 18 hours lecture.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 72D - Technical Elementary Algebra D

**1 unit**

This course provides a survey of computational and elementary algebraic processes with an emphasis on applications in the automotive and welding trades. Topics covered include, but are not limited to: the rectangular coordinate system, linear equations in two variables, and systems of linear equations. This course cannot be used as a prerequisite for Math 50 Core Intermediate Algebra or Math 55 Intermediate Algebra. Prerequisite: MATH 72B with a minimum grade of C and MATH 72C with a minimum grade of C. 18 hours lecture.

- Degree Applicable, Credit
- Grading Option: OP

### MATH 100C - Concurrent Support for SLAM Mathematics

**1 unit**

Concurrent Support for SLAM Math is for students interested in disciplines that require Statistics and Liberal Arts Mathematics (SLAM) courses. This course offers structured support to students who are concurrently enrolled in a first-level transfer course, such as Statistics and Mathematics for Liberal Arts, and Finite Mathematics. The support course includes material to prepare students for the rigor of the transfer math course by teaching learning skills necessary to succeed in college courses as well as review of relevant prerequisite algebraic and geometric concepts, and more in-depth investigation of core concepts in their concurrent math course. Corequisite: MATH 40 or MATH 47 or MATH 33. 54 hours laboratory.

- Non-Degree Applicable, Credit
- Grading Option: P/NP

### MATH 101C - Concurrent Support for BSTEM Mathematics

**1 unit**

Concurrent Support for BSTEM Mathematics is for students interested in Business, Science, Technology, Engineering and Mathematical fields. This course offers structured support to students who are concurrently enrolled in a first-level transfer course, such as College Algebra, Trigonometry, and Business Calculus. The support course includes material to prepare students for the rigor of the transfer math course by teaching learning skills necessary to succeed in college courses as well as review of relevant prerequisite algebraic and geometric concepts, and more in-depth investigation of core concepts in their concurrent math course. Corequisite: MATH 30 or MATH 39 or MATH 34. 54 hours laboratory.

- Non-Degree Applicable, Credit
- Grading Option: P/NP

### MATH 107 - Pre-Algebra

**4 units**

This course is intended to serve as a bridge between arithmetic and Elementary Algebra. It includes a review of arithmetic, operations involving signed integers, fractions, and decimals, variables and variable expressions, simple linear equations and their graphs, percent and proportion, introduction to statistics, geometry and measurement, and application problems. 54 hours lecture, 54 hours laboratory.

- Non-Degree Applicable, Credit
- Grading Option: OP

### MATH 110 - Elementary Algebra

**4 units**

Elementary algebra concepts, including: real numbers and their properties; algebraic expressions; integer exponents; operations with polynomial expressions; linear and quadratic equations; linear inequalities and set notation; graphs of linear equations and inequalities; slope; systems of linear equations and inequalities; and modeling with linear and quadratic equations. Strongly Recommended: MATH 107 with a minimum grade of C or MATH 107B with a minimum grade of C or NMAT 207 with a minimum grade of C. 72 hours lecture.

- Non-Degree Applicable, Credit
- Grading Option: OP

### MATH 110C - Concurrent Support for Elementary Algebra

**1 unit**

This course is concurrent support for Elementary Algebra. The course is designed to provide additional, formal support to students who are currently taking an Elementary Algebra. It includes a review of arithmetic, algebraic and geometric concepts that are relevant to their Elementary Algebra course, study strategies that promote understanding and improve performance, and more in-depth investigation of core concepts that are difficult for students to master. Embedded are learning skills such as growth mindset, brain research, time management, study skills, test taking, math anxiety and more. Corequisite: MATH 110 or NMAT 210. 54 hours laboratory.

- Non-Degree Applicable, Credit
- Grading Option: P/NP

### MATH 156 - Geometry

**3.5 units**

Topics include congruence, similarity, right triangles, trigonometry, circles, expressing geometric properties with equations, geometric measurement and dimension, modeling with geometry, conditional probability and the rules of probability, and using probability to make decisions. Prerequisite: MATH 110 with a minimum grade of C or NMAT 210 with a minimum grade of C. 54 hours lecture, 27 hours laboratory.

- Non-Degree Applicable, Credit
- Grading Option: OP

Independent Study

0.5 - 2 units

Independent Study courses are open to all students and employ many combinations of media and educational techniques to create individualized, self-pacing education. Check with the Counseling Center, Building 1600, concerning transferability of Independent Study courses to four-year institutions. Independent Study is contracted through an instructor for research, field experience, or skill development. Independent Study is offered under many subject areas contained in the Catalog using the number 29. Transfer: CSU; UC credit may be granted only after review of course outline by specific UC campus after transfer. Independent Study courses have a grading option of "OP" unless otherwise indicated.

- Degree Applicable, Credit