# Mathematics and Statistics

## Overview

The mathematics program provides students the opportunity to complete the lower-division coursework required for four-year programs in mathematics. For students who plan to transfer, completion of the CSU General-Breadth or IGETC general education pattern is encouraged. It is highly recommended that students meet with a counselor because major and general education requirements vary for each college/university. These courses also fulfill general education requirements for allied health, biological sciences, physical sciences, computer science and engineering.

Learn about math and statistics placement.

## Career Options

Mathematicians work as statisticians, analysts, computer programmers, actuaries, researchers, planners and educators. The mathematics program provides students the opportunity to complete the lower-division coursework required for four-year programs in mathematics.

- Dean Angelena Lambert
- Department Chair Matthew Schutte
- Meta Major Science, Math, and Engineering
- Math Integration Bee Math Program Integration Bee
- Phone (916) 558-2202
- Email LeeL@scc.losrios.edu

## Associate Degrees for Transfer

### A.S.-T. in Mathematics

The mathematics program provides students the opportunity to complete the lower-division coursework required for four-year programs in mathematics. This program is for students who plan to transfer to a California State University (CSU). Completion of the CSU General-Breadth or IGETC general education pattern is required. It is highly recommended that students meet with a counselor because major and general education requirements vary for each college/university.

The Associate Degree for Transfer (ADT) student completion requirements (as stated in SB1440 law):

(1) Completion of 60 semester units or 90 quarter units that are eligible for transfer to the California State University, including both of the following:

(A) The Intersegmental General Education Transfer Curriculum (IGETC) or the California State University General Education-Breadth Requirements (CSU GE-Breadth).

(B) A minimum of 18 semester units or 27 quarter units in a major or area of emphasis, as determined by the community college district.

(2) Obtainment of a minimum grade point average of 2.0.

ADTs also require that students must earn a “C” or better in all courses required for the major or area of emphasis. A "P" (Pass) grade is also an acceptable grade for courses in the major if the course is taken on a Pass/No Pass basis.

**Catalog Date:** August 1, 2023

#### Degree Requirements

Course Code | Course Title | Units |
---|---|---|

MATH 400 | Calculus I | 5 |

MATH 401 | Calculus II | 5 |

MATH 402 | Calculus III | 5 |

MATH 410 | Introduction to Linear Algebra | 3 |

MATH 420 | Differential Equations | 4 |

Total Units: | 22 |

*The Associate in Science in Mathematics for Transfer (AS-T) degree may be obtained by completion of 60 transferable,
semester units with a minimum overall grade point average (GPA) of 2.0, including (a) a minimum grade of "C" (or "P") for each course in the major or area
of emphasis described in the Required Program, and (b) either the
Intersegmental General Education Transfer Curriculum (IGETC) or the
California State University General Education-Breadth Requirements.*

#### Student Learning Outcomes

Upon completion of this program, the student will be able to:

- explain and apply basic concepts of single variable calculus including various forms of derivatives and integrals, their interconnections, and their uses in analyzing and solving real-world problems.
- explain and apply basic concepts of multivariable calculus, linear algebra, or differential equation techniques, their interconnections, and their uses in analyzing and solving real-world problems.
- write logical proofs of basic theorems.

#### Career Information

Mathematicians work as statisticians, analysts, computer programmers, actuaries, researchers, planners, and educators. This major is designed to meet the lower-division requirements for most bachelor's degrees in Mathematics.

## Associate Degrees

### A.S. in Mathematics

The mathematics program provides students the opportunity to complete the lower-division coursework required for four-year programs in mathematics. For students who plan to transfer, completion of the CSU General-Breadth or IGETC general education pattern is encouraged. It is highly recommended that students meet with a counselor because major and general education requirements vary for each college or university. These courses also fulfill general education requirements for allied health, biological sciences, physical sciences, computer science, and engineering.

Note: Students planning to transfer to four-year institutions are advised to meet with a counselor for general education requirements.

Note: The University of California has a credit restriction on certain combinations of mathematics courses. See counselor for detailed information on current UC Transferable Course Agreement.

**Catalog Date:** August 1, 2023

#### Degree Requirements

Course Code | Course Title | Units |
---|---|---|

MATH 400 | Calculus I | 5 |

MATH 401 | Calculus II | 5 |

MATH 402 | Calculus III | 5 |

MATH 410 | Introduction to Linear Algebra | 3 |

MATH 420 | Differential Equations | 4 |

A minimum of 3 units from the following: | 3 | |

CISP 301 | Algorithm Design and Implementation (4) | |

CISP 360 | Introduction to Structured Programming (4) | |

CISP 400 | Object Oriented Programming with C++ (4) | |

CISP 401 | Object Oriented Programming with Java (4) | |

ENGR 405 | Engineering Problem Solving (3) | |

PHIL 325 | Symbolic Logic (3) | |

STAT 300 | Introduction to Probability and Statistics (4) | |

or STAT 480 | Introduction to Probability and Statistics - Honors (4) | |

Total Units: | 25 |

*The Mathematics Associate in Science (A.S.) degree may be obtained by completion of the required program, plus general education requirements, plus sufficient electives
to meet a 60-unit total. See SCC graduation requirements.*

#### Student Learning Outcomes

Upon completion of this program, the student will be able to:

- explain and apply basic concepts of single variable calculus including various forms of derivatives and integrals, their interconnections, and their uses in analyzing and solving real-world problems.
- explain and apply basic concepts of multivariable calculus, linear algebra, or differential equation techniques, their interconnections, and their uses in analyzing and solving real-world problems.
- write logical proofs of basic theorems.
- analyze and evaluate various theoretical and real-world problems and analyze existing solutions or create and evaluate novel solutions using mathematics, logic, and technology as appropriate.

#### Career Information

Mathematicians work as statisticians, analysts, computer programmers, actuaries, researchers, planners, and educators. This major is designed to meet the lower-division requirements for most bachelor's degrees in Mathematics.

## Mathematics (MATH) Courses

### MATH 27 Self-Paced Basic Skills Mathematics

- Units:0.5 - 2
- Hours:27 - 108 hours LAB
- Prerequisite:None.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED.

This is a self-paced course in basic mathematics skills including the basic operations of addition, subtraction, multiplication, and division applied to the whole numbers, fractions, and decimals. This course is graded Pass/No Pass. Credit is earned in one-half unit increments and is dependent on progress in the course and class participation. This is an open-entry/open-exit course which may be taken for a maximum of two units. This course does not fulfill the learning skills requirement for graduation.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO 1: CORRECTLY USE THE ORDER OF OPERATIONS TO EVALUATE EXPRESSIONS. ACCURATELY COMPUTE PROBLEMS INVOLVING THE BASIC OPERATIONS OF ARITHMETIC (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTS, ORDER OF OPERATIONS) ON WHOLE NUMBERS, FRACTIONS, AND DECIMALS.
- 1a: identify the prime numbers from 2 to 50. Use divisibility tests, factorization, and the concept of prime and composite to construct the least common multiple. Understand the process of rewriting a given number as the product of all distinct prime numbers.
- 1b: express numeric information in one of the following three forms: fraction, percent, decimal.
- 1c: incorporate concepts of prime factorization and greatest common factor to simplify fractions.
- 1d: evaluate problems involving ratios, proportions, and percents.
- 1e: perform unit conversions for American measurements which involve length, capacity, weight, and times. Use the method of unit conversions to solve application problems.
- 1f: demonstrate concepts of rounding and estimation of whole numbers and decimals to nearest place value.
- SLO 2: DEMONSTRATE THE ABILITY TO TRANSLATE MATHEMATICAL PROBLEMS IN WORD FORM TO AN EXPRESSION OR SINGLE VARIABLE EQUATION, AND SOLVE SINGLE VARIABLE ONE-STEP EQUATIONS.
- 2a: translate simple English phrases and sentences into simple algebraic expressions and equations.
- 2b: construct equations by translating information from word form to symbolic form with the use of a variable.
- 2c: set up applied problems involving ratios, proportions, and percent.
- 2d: calculate solutions of one-step single variable equations.
- 2e: solve applications problems involving whole numbers, fractions, decimals, ratios, proportions, and percent.
- 2f: find perimeter and area of basic Euclidean and compound shapes.
- SLO 3: ANALYZE PATTERNS AND ORGANIZE MATHEMATICAL THOUGHTS TO INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.
- ~ Apply mathematical concepts and patterns to new problems and new situations.
- ~ Demonstrate ability to communicate mathematically by writing and presenting the work of the problems in an organized way.

### MATH 28 Basic Skills Mathematics

- Units:3
- Hours:54 hours LEC; 18 hours LAB
- Prerequisite:None.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This is a lecture course with lab time in basic mathematics skills including the basic operations of addition, subtraction, multiplication, and division applied to the whole numbers, fractions, and decimals. This course does not fulfill the learning skills requirement for graduation.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO 1: CORRECTLY USE THE ORDER OF OPERATIONS TO EVALUATE EXPRESSIONS. ACCURATELY COMPUTE PROBLEMS INVOLVING THE BASIC OPERATIONS OF ARITHMETIC (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTS, ORDER OF OPERATIONS) ON WHOLE NUMBERS, FRACTIONS, AND DECIMALS.
- ~Identify the prime numbers from 2 to 50. Use divisibility tests, factorization, and the concept of prime and composite to construct the least common multiple. Understand the process of rewriting a given number as the product of all distinct prime numbers.
- ~Express numeric information in one of the following three forms: fraction, percent, decimal.
- ~Incorporate concepts of prime factorization and greatest common factor to simplify fractions.
- ~Evaluate problems involving ratios, proportions, and percents.
- ~Perform unit conversions for American measurements which involve length, capacity, weight, and times. Use the method of unit conversions to solve application problems.
- ~Demonstrate concepts of rounding and estimation of whole numbers and decimals to nearest place value.
- SLO 2: DEMONSTRATE THE ABILITY TO TRANSLATE MATHEMATICAL PROBLEMS IN WORD FORM TO AN EXPRESSION OR SINGLE VARIABLE EQUATION, AND SOLVE SINGLE VARIABLE ONE-STEP EQUATIONS.
- ~Translate simple English phrases and sentences into simple algebraic expressions and equations.
- ~Construct equations by translating information from word form to symbolic form with the use of a variable.
- ~Set up applied problems involving ratios, proportions, and percents.
- ~Calculate solutions of one-step single variable equations.
- ~Solve applications problems involving whole numbers, fractions, decimals, ratios, proportions, and percents.
- ~Find perimeter and area of basic Euclidean and compound shapes.
- SLO 3: ANALYZE PATTERNS AND ORGANIZE MATHEMATICAL THOUGHTS TO INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.
- ~Apply mathematical concepts and patterns to new problems and new situations.
- ~Demonstrate ability to communicate mathematically by writing and presenting the work of the problems in an organized way.

### MATH 34 Pre-algebra

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 28 with a “C” or better, or completion of the MATH 27 curriculum (80% or higher on all six chapter tests), or placement through the assessment process.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. The emphasis in this course will be on skills necessary for success in elementary algebra. Course content will include review of fundamentals of arithmetic including whole numbers, common fractions, decimal fractions, and percentages. Other topics include order of operations, signed numbers, complex fractions, exponents, and scientific notation. There will be an introduction to the algebra of polynomials and/or an introduction to graphing lines, as time permits.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO 1: ARTICULATE THE IMPORTANCE OF THE ORDER OF OPERATIONS AND HOW THEY RELATE TO THE REAL NUMBER SYSTEM, EXPRESSIONS, EQUATIONS AND EVALUATION OF MATHEMATICAL FORMULAS.
- ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
- ~ Multiply and divide numbers expressed in scientific notation.
- ~ Simplify expressions involving variables by adding, subtracting, multiplying, dividing, or reducing.
- ~ Use and evaluate formulas with more than one variable.
- ~ Demonstrate accurate use of the properties of real numbers and the exponent rules in addition, subtraction, and multiplication of polynomials.
- SLO 2: DEMONSTRATE THE ABILITY TO RECOGNIZE KEY WORDS OR PHRASES THAT WOULD GUIDE ONE THROUGH THE TRANSLATION OF A MATHEMATICAL PROBLEM IN WORD FORM TO AN ALGEBRAIC EXPRESSION OR EQUATION.
- ~ Solve applied problems using signed numbers, variable expressions, scientific notation, and equations.
- ~ Solve linear equations in one variable involving signed numbers, fractions, and decimals.
- ~ Directly translate equations in word form to symbolic form with the use of variables and solve them.
- SLO 3: INVESTIGATE AND MODEL REAL LIFE PHENOMENA THROUGH THE USE OF LINEAR EQUATIONS IN TWO VARIABLES AND THEIR CORRESPONDING GRAPHS (ALGEBRAICALLY AND GEOMETRICALLY), AND THINK CRITICALLY ABOUT HOW THE MATHEMATICS IS RELEVANT TO ONE’S LIFE.
- ~ Find solutions to linear equations in two variables and plot these points on the two-dimensional coordinate system.
- ~ Interpret graphs of two-dimensional data, such as bar graphs, line graphs, and pie charts.
- SLO 4: UTILIZE AND APPLY THE METHOD OF DIMENSIONAL ANALYSIS (OR UNIT ANALYSIS) TO COMPARE AND CONVERT QUANTITIES.
- ~ Solve applied problems using measurement conversions, proportions, and percent.
- ~ Perform accurate computations involving measurement conversion.
- SLO 5: DEMONSTRATE THE ABILITY TO RECOGNIZE PATTERNS, ORGANIZE MATHEMATICAL THOUGHTS, AND INCREASE THE LEVEL OF ABSTRACT THINKING THAT IS ESSENTIAL FOR REAL-LIFE PROBLEM-SOLVING.

### MATH 100 Elementary Algebra

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 34 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course includes the fundamental concepts and operations of algebra with problem solving skills emphasized throughout. Topics include properties of real numbers, linear equations and inequalities, integer exponents, polynomials, polynomial factorization, rational expressions and equations, radical expressions and equations, rational exponents, systems of linear equations and inequalities, the rectangular coordinate system, graphs and equations of lines, and quadratic equations.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO#1: Use increased computational skills and number sense, recognize the order of operations and properties of real numbers; include evaluating various mathematical formulas and extending operations to variable expressions and combining like terms
- ~ Simplify expressions using the order of operations and basic properties of real numbers.
- ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
- ~ Multiply and divide numbers expressed in scientific notation.
- ~ Use and evaluate formulas with more than one variable.
- SLO#2: Solve first-degree equations, inequalities, and applications.
- ~ Identify the types of equations including conditional equations, contradiction, and identity and techniques for their solution.
- ~ Solve linear inequalities and write the solution in both set-builder and interval notation.
- ~ Apply problem-solving skills to construct equations and inequalities for application problems and solve the applications by solving the equations or inequalities and appropriately interpreting the results.
- SLO#3: Identify and analyze linear equations, and graphs of linear equations and linear inequalities.
- ~ Interpret the slope of a line as a rate of change and graph a line.
- ~ Generate an algebraic model for data that follows linear behavior and interpret the result of this model. Applications of linear models include linear growth, linear depreciations, and rates.
- SLO#4: Apply mathematical terminology, symbols and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
- ~ Evaluate and expand polynomial expressions and expressions written in scientific notation.
- ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
- ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
- ~ Use operations on polynomials to solve certain polynomial equations and applications.
- SLO#5: Identify prime polynomials and factor polynomials into primes using various techniques.
- ~ Factor out common factors and factor by grouping.
- ~ Factor the difference of two squares and factor trinomials including perfect square trinomials.
- ~ Solve polynomial equations by factoring and using the zero factor property.
- ~ Think critically and abstractly by modeling an application problem using a polynomial equation to solve and interpret the result.
- SLO#6: Simplify, combine and evaluate rational expressions using the operations of arithmetic.
- ~ Multiply and divide rational expressions and incorporate factoring to simplify to lowest terms.
- ~ Add and subtract rational expressions using the algebraic method and least common denominator.
- ~ Solve rational equations by multiplying by the least common denominator.
- ~ Use an appropriate rational equation to model an application problem to solve and interpret the results.
- SLO #7: Solve systems of linear equations and systems of linear inequalities as well as their applications and effectively organize, present, and summarize the quantitative information using algebraic, numerical and graphical methods.
- ~ Calculate the solution to a 2x2 system of linear equations using the methods of graphing, substitution, and elimination and identify the types of 2x2 systems.
- ~ Construct a system of linear equations for applications and solve the applications by solving the system and appropriately interpret the solution.
- ~ Compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.
- SLO#8: Demonstrate with proficiency how to use arithmetic operations on radicals and simplify radical expressions.
- ~ Simplify different types of radicals, rationalize denominators and combine radicals when it is appropriate.
- ~ Solve radical equations and evaluate radical expressions.
- ~ Solve applied problems using radical equations and using the Pythagorean Theorem to solve triangles and applications.
- ~ Verify how to extend the definition of an exponent to a rational exponent and interpret a rational exponent as a radical.
- ~ Use radicals to solve quadratic equations by taking roots, completing the square, and using the quadratic formula, and employ quadratic equations in various applications.

### MATH 103 Elementary Algebra, Part I

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 34 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course will cover the first half of the traditional MATH 100 course. Topics include: properties of real numbers, linear equations and inequalities, integer exponents, polynomials, systems of linear equations and inequalities, the rectangular coordinate system, graphs and equations of lines, and applications.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO#1: Use increased computational skills and number sense, recognize the order of operations and properties of real numbers; include evaluating various mathematical formulas and extending operations to variable expressions and combining like terms
- ~Simplify expressions using the order of operations and basic properties of real numbers.
- ~ Compute with accuracy problems involving the basic operations of arithmetic (addition, subtraction, multiplication, division, exponents, order of operations) on signed numbers.
- ~ Multiply and divide numbers expressed in scientific notation.
- SLO#2: Solve first-degree equations, inequalities, and applications.
- ~Identify the types of equations including conditional equations, contradiction, and identity and techniques for their solution.
- ~Solve linear inequalities and write the solution in both set-builder and interval notation.
- ~ Apply problem-solving skills to construct equations and inequalities for application problems and solve the applications by solving the equations or inequalities and appropriately interpreting the results.
- SLO#3: Identify and analyze linear equations, and graphs of linear equations and linear inequalities.
- ~ Interpret the slope of a line as a rate of change and graph a line.
- ~ Generate an algebraic model for data that follows linear behavior and interpret the result of this model. Applications of linear models include linear growth, linear depreciation, and rates.
- SLO#4: Apply mathematical terminology, symbols and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
- ~ Evaluate and expand polynomial expressions and expressions written in scientific notation.
- ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
- ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
- ~ Use operations on polynomials to solve certain polynomial equations and applications.
- SLO #5: Solve systems of linear equations and systems of linear inequalities as well as their applications and effectively organize, present, and summarize the quantitative information using algebraic, numerical and graphical methods.
- ~ Calculate the solution to a 2x2 system of linear equations using the methods of graphing, substitution, and elimination and identify the types of 2x2 systems.
- ~ Construct a system of linear equations for applications and solve the applications by solving the system and appropriately interpret the solution.
- ~ Compute the solution to a system of linear inequalities using a graph and describe the meaning of this solution.

### MATH 104 Elementary Algebra, Part II

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 103 with a grade of "C" or better
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course covers the second half of the traditional MATH 100 course. Topics include: polynomial factorization, rational expressions and equations, radical expressions and equations, rational exponents, quadratic equations, and applications.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- SLO#1: Apply mathematical terminology, symbols, and operations to develop and extend arithmetic operations on polynomials and to evaluate polynomial expressions.
- ~ Apply rules of exponents (including negative exponents) to simplify algebraic expressions.
- ~ Demonstrate proficiency in all arithmetic operations on polynomials, particularly multiplying using FOIL.
- ~ Use operations on polynomials to solve certain polynomial equations and applications.
- SLO#2: Identify prime polynomials and factor polynomials into primes using various techniques.
- ~ Factor out common factors and factor by grouping.
- ~ Factor the difference of two squares and factor trinomials including perfect square trinomials.
- ~ Solve polynomial equations by factoring and using the zero factor property.
- ~ Think critically and abstractly by modeling an application problem using a polynomial equation to solve and interpret the result.
- SLO#3: Simplify, combine and evaluate rational expressions using the operations of arithmetic.
- ~ Multiply and divide rational expressions and incorporate factoring to simplify to lowest terms.
- ~ Add and subtract rational expressions using the algebraic method and least common denominator.
- ~ Solve rational equations by multiplying by the least common denominator.
- ~ Use an appropriate rational equation to model an application problem to solve and interpret the results.
- SLO#4: Demonstrate with proficiency how to use arithmetic operations on radicals and simplify radical expressions.
- ~ Simplify different types of radicals, rationalize denominators and combine radicals when it is appropriate.
- ~ Solve radical equations and evaluate radical expressions.
- ~ Solve applied problems using radical equations and using the Pythagorean Theorem to solve triangles and applications.
- ~ Verify how to extend the definition of an exponent to a rational exponent and interpret a rational exponent as a radical.
- ~ Use radicals to solve quadratic equations by taking roots, completing the square, and using the quadratic formula, and employ quadratic equations in various applications.

### MATH 109 Fundamentals of Algebra for Liberal Arts Mathematics and Statistics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 34 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course consists of elements of beginning and intermediate algebra needed for STAT 300, MATH 300, or MATH 310. Topics include modeling using expressions, equations, functions, and graphs; polynomial inequalities. Note: This course is not intended for students pursuing business or STEM majors and who plan to take courses in science, computer information science, engineering, mathematics, physics, chemistry, business or economics.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve linear, quadratic, absolute value, square root, exponential, logarithmic equations.
- solve systems of linear equations in two variables and linear and absolute value inequalities.
- graph linear, quadratic, absolute value, exponential, and logarithmic functions.
- apply elementary operations on functions.
- use mathematical modeling to solve applications.

### MATH 110 Elementary Geometry

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 or 104 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course introduces Euclidean Geometry. Topics include sets, definitions, postulates, theorems, deductive and inductive reasoning, proof, parallel lines, triangles, polygons, congruence, similarity, constructions, the Pythagorean Theorem, right triangle trigonometry, circles, analytic geometry, and elementary solid geometry.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- clearly state and correctly use definitions, postulates, and theorems of Euclidean geometry.
- compute segment lengths and angle measures of geometric objects using definitions, postulates, and theorems of Euclidean geometry.
- apply appropriate formulas when finding areas of planar figures, surface area and volume of solids, and when analyzing diagrams in the Cartesian coordinate system.
- perform geometric constructions using a straightedge and compass.
- write direct proofs and analytic proofs using the definitions, postulates, and theorems of Euclidean geometry.

### MATH 120 Intermediate Algebra

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 100 or 104 with a grade of "C" or better, or placement through the assessment process.
- General Education:AA/AS Area II(b)
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course reviews and extends the concepts of elementary algebra, with problem solving skills emphasized throughout. Topics that are reviewed and extended include linear and quadratic equations, factoring polynomials, rational expressions, exponents, radicals, equations of lines, and systems of equations. New topics include graphs and their translations and reflections, functions, exponential and logarithmic functions, graphs of quadratic functions, conic sections, nonlinear systems of equations, polynomial, rational, and absolute value inequalities, sequences, series, and the Binomial Theorem.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
- solve systems of equations and solve linear, polynomial, rational, and absolute value inequalities.
- use the definition of a function to determine if a relation is a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
- sketch the graphs of basic functions, quadratic functions, transformations of these functions, and conic sections.
- apply algebraic methods when solving word problems.

### MATH 123 Intermediate Algebra, Part I

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 100 or 104 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course will cover the first half of the traditional MATH 120 course. Topics include solving linear equations and inequalities, factoring of polynomials, rational expressions, exponents, radicals, solving equations containing rational and radical expressions, equations of lines, functions and absolute value equations and inequalities, and complex numbers.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify expressions and solve equations involving absolute values, polynomials, rational expressions, and radicals.
- solve linear and absolute value inequalities.
- define functions, use function notation, and perform the four arithmetic operations on functions.
- sketch the graphs of basic functions and transformations of the functions.
- apply algebraic methods when solving word problems.

### MATH 124 Intermediate Algebra, Part II

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 123 with a grade of "C" or better
- General Education:AA/AS Area II(b)
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course will cover the second half of the traditional MATH 120 course. Topics include quadratic expressions, equations, inequalities and graphs, conic sections, linear and nonlinear systems of equations, composite and inverse functions, exponential and logarithmic functions, and sequences and series.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve quadratic equations using a variety of methods, solve exponential and logarithmic equations, and solve equations quadratic in form.
- solve linear and nonlinear systems of equations and solve polynomial and rational inequalities.
- find composite and inverse functions.
- graph quadratic functions, conic sections, exponential functions, and logarithmic functions, including transformations.
- apply algebraic methods when solving word problems.

### MATH 140 Mathematics Competency

- Units:4
- Hours:72 hours LEC
- General Education:AA/AS Area II(b)
- Catalog Date:August 1, 2023

In compliance with CA Legislation AB 705 and AB 1705, THIS COURSE IS NOT CURRENTLY BEING OFFERED. This course introduces students to everyday uses of mathematics. Topics will include measurement systems, reasoning and logic, elections, inflation and other indexes, chance and risk, and finances. One or more modules of mathematical interest from career technical programs and contemporary careers including but not limited to nursing, occupational therapy, flight technology, and cosmetology will be integrated into the course.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- choose appropriate mathematical models for analyzing democratic and social phenomenon.
- compare and choose among financial options such as loans and annuities or make other relevant financial decisions.
- compute and compare risk factors in various situations.
- create visual and graphical representations of data relevant to topics.
- compute unit conversions in various contexts.
- explain positions on topics using valid arguments.
- demonstrate the use of mathematics and critical thinking in contemporary vocational and technical fields.

### MATH 170 Algebra Review for Calculus

- Units:2
- Hours:36 hours LEC
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is a review of college preparatory high school algebra. It includes the necessary skills for success in higher mathematics courses including calculus. Topics include real numbers, linear equations and inequalities, properties of lines, absolute values, polynomials and factoring, rational expressions, exponents, quadratic equations, and functions.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- demonstrate preparedness for subsequent UC Davis mathematics courses such as precalculus or calculus. The students will place into the next mathematics course based on scores from the UCD Mathematics Placement Exam, which they will take upon completion of MATH 170.
- solve mathematical problems involving polynomials, rational expressions, equations and inequalities, exponents, radical, and logarithms and demonstrate conceptual rather than strictly procedural knowledge of these topics.
- demonstrate increased competence in problem solving, including application problems, and a higher level of mathematical maturity.
- model substantive interpretation of algebraic problems.

### MATH 295 Independent Studies in Mathematics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is an independent studies course. The topics are to be arranged between the instructor and the student.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- demonstrate understanding of the mathematical concepts studied in the course.
- demonstrate competence in the mathematical skills studied in the course.

### MATH 299 Experimental Offering in Mathematics

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is the experimental courses description.

### MATH 300 Introduction to Mathematical Ideas

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 109, 120, or 124 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- Catalog Date:August 1, 2023

This course is intended to help the non-Mathematics major student relate to the spirit of mathematics through a study of some engaging ideas of mathematics. Several specific topics will be chosen from: numeration systems, logic, sets, number theory, algebraic modeling, geometry, combinatorics, probability, statistics, consumer mathematics, graph theory, voting and apportionment, matrices, and perhaps others. This course is not recommended for students entering elementary school teaching or for business administration majors.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- analyze inferences and conjectures present in a variety of mathematical ideas and systems.
- construct well written solutions to mathematical exercises.
- apply critical thinking skills developed in studying a mathematical topic to issues that transcend mathematics.
- research and demonstrate an understanding of and explain mathematical ideas that are at an appropriate skill level.

### MATH 310 Mathematical Discovery

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 110 and either MATH 109 or MATH 120 with grades of "C" or better or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4
- Catalog Date:August 1, 2023

This course is designed to introduce students to the spirit of mathematics by involving them in aspects of mathematical processes of exploration, conjecture, and proof. Students will examine mathematical patterns and relations, formulate conjectures, and prove their conjectures. Educational standards (e.g. Common Core) and issues are a focus throughout the content of the course. Areas of mathematics from which content may be derived include number theory, statistics, probability, geometry, and sequences and series. This course is recommended for students interested in a career in education.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- explain mathematical relationships inherent in problems and situations.
- make conjectures about mathematical relationships and content.
- prove or disprove conjectures about mathematical relationships and content.
- develop an appreciation of mathematical relevance to every day life.
- analyze documents directing the study of mathematics in American schools, as well as the strategies, procedures, and emphases advocated in those documents.

### MATH 333 Introduction to College Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:Through the Los Rios Placement Process or High School Algebra 2 or Integrated Math 3 or Intermediate Algebra.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; IGETC Area 2
- Catalog Date:August 1, 2023

This course is a transfer-level college algebra course for majors in the Liberal Arts or for BSTEM students needing to further their algebra skills before taking pre-calculus-level coursework. Topics include absolute value, polynomial, rational, radical, exponential, and logarithmic functions; solving equations involving these functions; graphing these functions using rigid and non-rigid transformations; solving linear and nonlinear inequalities; systems of equations; complex numbers; and inverse functions.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- analyze and investigate properties of functions.
- synthesize results from the graphs and/or equations of functions.
- solve and apply equations including rational, linear, absolute value, polynomial, exponential, and logarithmic equations.
- solve linear and nonlinear systems of equations and inequalities.
- use functions and other algebraic techniques to model real world applications.
- demonstrate the relationship between functions and their inverses graphically and algebraically.
- apply transformations to the graphs of functions.

### MATH 340 Calculus for Business and Economics

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 120 or 124 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 140
- Catalog Date:August 1, 2023

The content of this course includes review of the logarithmic and exponential functions, intuitive introduction to limits, and development of the derivative and definite integral. Application of these concepts to economics and business will be emphasized.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- find the derivatives of polynomial, rational, exponential, and logarithmic functions.
- find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
- sketch the graphs of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity, and points of inflection.
- analyze the marginal cost, profit, and revenue when given the appropriate function.
- determine maxima and minima in optimization problems using the derivative.
- use derivatives to find rates of change and tangent lines.
- use calculus to analyze revenue, cost, and profit.
- find definite and indefinite integrals by using the general integral formulas, integration by substitution, and other integration techniques.
- use integration in business and economics applications.

### MATH 342 Modern Business Mathematics

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 120 or 124 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- Catalog Date:August 1, 2023

This course is designed around applications of mathematics in economic and business contexts. Specific topics will include functions and related business formulas, tables and graphs, finance (interest, annuities, and exponential models in economics), rates of change including applications and optimization, and linear programming.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- analyze formulas, tables, graphs, and data sets in order to form conclusions or make predictions.
- calculate both present and future values involving compound interest and annuities.
- analyze applications of annuities involving loan amortization and sinking funds, applying necessary formulas.
- identify and graph linear, quadratic, power, polynomial, exponential, and logarithmic functions.
- formulate and apply exponential growth or decay functions pertaining to business applications.
- evaluate rates of change for a variety of elementary functions and apply them to marginal analysis.
- find and interpret optimum values related to business applications.
- solve linear programming problems using a graphical approach.

### MATH 355 Calculus for Biology and Medicine I

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 373 with a grade of "C" or better, or placement through the assessment process.
- Advisory:MATH 372 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- Catalog Date:August 1, 2023

This course is an introduction to differential calculus and elementary differential equations via applications in biology and medicine. It covers limits, derivatives of polynomials, trigonometric and exponential functions, graphing, and applications of the derivative to biology and medicine. Topics include the Fundamental Theorem of Calculus and techniques of integration, including integral tables and numerical methods. This course does not meet the prerequisite for PHYS 410.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- simplify algebraic and trigonometric expressions as they appear in calculus computations.
- compute limits and discuss the continuity of a given function.
- apply differentiation and integration techniques to algebraic, exponential, logarithmic, and trigonometric functions.
- apply differentiation techniques to curve sketching and optimization problems.
- solve problems in biology and medicine involving exponential, logarithmic, and trigonometric functions through the application of calculus techniques.
- apply the Fundamental Theorem of Calculus to the evaluation of definite integrals.
- solve separable and first-order linear differential equations.
- interpret results of the analysis of mathematical modeling in applications of population growth or decay, manufacturer and consumer perspectives, chemical mixtures and reactions, and other course topics.

### MATH 356 Calculus for Biology and Medicine II

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 355 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- Catalog Date:August 1, 2023

This course is the continuation of MATH 355. It covers matrix algebra with eigenvalues and eigenvectors, systems of linear equations, functions of several variables, partial derivatives, systems of differential equations, probability, and applications to biology and medicine. This course does not meet the prerequisite for PHYS 410 or PHYS 420.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- calculate double integrals.
- calculate partial derivatives of functions of several variables and calculate and explain the significance of extrema of these functions in applied settings.
- analyze surfaces and graph functions of two variables in the three-dimensional coordinate system.
- devise models and solve linear systems of ordinary differential equations.
- evaluate and apply the chain rule, directional derivatives, and gradient vectors for functions of several variables.
- analyze results of computing eigenvalues and eigenvectors.
- compute counts and probabilities in a variety of experimental events.
- compute and apply Bayes' Formula.

### MATH 372 College Algebra for Calculus

- Units:4
- Hours:72 hours LEC
- Prerequisite:Intermediate Algebra or equivalent with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- Catalog Date:August 1, 2023

This course provides a rigorous treatment of college-level algebra and its applications, with a particular focus on preparing students for the calculus sequence for Science, Technology, Engineering, and Mathematics (STEM) majors. Topics include polynomial, rational, radical, exponential, absolute value, and logarithmic functions, graphs, and equations; systems of equations; the theory of polynomial equations; analytic geometry including conics; sequences and series; and mathematical induction. Emphasis is given to analytical reasoning and problem-solving. This course may be taken concurrently with MATH 373, Trigonometry for Calculus. Completion of both MATH 372 AND MATH 373 with grades of "C" or better meets the prerequisite for MATH 400, Calculus I. The maximum UC transfer credit is 5 units for any combination of College Algebra and Precalculus courses.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve equations and inequalities and manipulate expressions.
- solve systems of equations and inequalities.
- demonstrate a deep understanding of functions and their properties.
- demonstrate a deep understanding of inverse functions and their algebraic and graphical relationship to their parent functions.
- graph a variety of curves (showing intercepts, asymptotes, vertices, etc.).
- solve application problems by creating and using mathematical models that involve synthesis of course concepts.

### MATH 373 Trigonometry for Calculus

- Units:4
- Hours:72 hours LEC
- Prerequisite:Intermediate Algebra or equivalent with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 851
- Catalog Date:August 1, 2023

This course provides a rigorous treatment of trigonometry and its applications, with a particular focus on preparing students for the calculus sequence for Science, Technology, Engineering, and Mathematics (STEM) majors. Topics include right triangle trigonometry, unit circle trigonometry, graphs of trigonometric functions, proofs of trigonometric identities, solving trigonometric equations, applications of trigonometric functions (laws of sines and cosines), inverse trigonometric functions, the polar coordinate system, and vectors. Emphasis is given to analytical reasoning and problem-solving. This course may be taken concurrently with MATH 372, College-Algebra for Calculus. Completion of both MATH 372 AND MATH 373 with grades of "C" or better meets the prerequisite for MATH 400, Calculus I. The maximum UC transfer credit is 5 units for any combination of College Algebra and Precalculus courses.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
- evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
- recognize, apply, and prove trigonometric identities and solve trigonometric equations.
- create and analyze graphs of trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
- convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
- apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.
- prove simple mathematical facts.

### MATH 400 Calculus I

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 372 and 373 with grades of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 210
- Catalog Date:August 1, 2023

This course explores the basic concepts of analytic geometry, limits (including indeterminate forms), derivatives, and integrals. The topics covered will include graphs, derivatives, and integrals of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions. Standard proofs will be covered, such as delta-epsilon proofs and proofs of some theorems. Applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, and optimization.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- determine limits of algebraic and transcendental functions using algebraic, graphical, and/or numerical methods
- determine derivatives of algebraic and transcendental functions.
- evaluate integrals of algebraic and transcendental functions.
- apply derivatives and integrals to solve physics, economic, geometric, and/or other application problems.
- write proofs related to limits, continuity, and differentiability, including delta-epsilon proofs.

### MATH 401 Calculus II

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 400 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 220
- Catalog Date:August 1, 2023

This course is a continuation of MATH 400. Topics covered will include techniques of integration, numerical integration, improper integrals, infinite series, parametric equations, polar equations, and possibly conic sections. Many applications will be covered including those involving areas between planar curves, volumes of revolution, work, moments, center of mass, average value, arc length, and surface area.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- evaluate integrals using a variety of integration techniques including integration by parts, partial fraction decomposition, trigonometric substitution and others.
- devise and evaluate integrals to find the volume and surface area of a solid of revolution, total work, the length of a curve, the center of mass of a solid, and other applications of integration.
- estimate integrals using numerical techniques.
- evaluate improper integrals.
- evaluate the calculus components of parametric and polar relations including finding tangent lines, areas, and arc lengths.
- prove convergence or divergence of sequences and series using Test for Divergence, Integral Test, p-Series Test, Comparison Tests, Alternating Series Test, Maclaurin and Taylor series, and power series.
- construct power series representations of functions, derivatives, and integrals and determine radius and intervals of convergence of power series.
- estimate and determine maximum errors in finding function values using infinite and finite power series.
- solve separable differential equations.

### MATH 402 Calculus III

- Units:5
- Hours:90 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 230
- Catalog Date:August 1, 2023

This course extends the concepts of limits, derivatives, and integrals to vector-valued functions and functions of more than one variable. The topics covered include three-dimensional analytic geometry and vectors, partial derivatives, multiple integrals, line integrals, surface integrals, and the theorems of Green, Gauss (Divergence), and Stokes. Many applications of calculus are included.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- find the distance between a point and a line, a point and a plane, two parallel planes, or two parallel and/or skew lines; find the equations of lines and planes.
- calculate the arc length and curvature at any point in the domain of the function for a space curve.
- compute a number of vector based function values on plane curves and space curves. These include velocity vectors, acceleration vectors, speed, curvature, arc-length, binormal vectors, unit tangent and unit normal vectors.
- find the limit of a multivariate function at a point or show that the limit does not exist.
- evaluate partial derivatives and directional derivatives. Find the extrema for functions of two variables; find the absolute maximum and absolute minimum values of a function defined on a closed boundary.
- evaluate double and triple integrals using rectangular, polar, cylindrical, and spherical coordinate systems as well as evaluating a double integral by employing a change of variables; calculate volumes, surface area, and other physical phenomena by applying double and triple integrals
- find the gradient of a scalar field and the divergence and curl of a vector field.
- evaluate line and surface integrals using Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.

### MATH 410 Introduction to Linear Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 250
- Catalog Date:August 1, 2023

This course is an introductory course in linear algebra. Topics include matrices, determinants, systems of equations, vector spaces, linear transformations, eigenvectors, and applications. Proofs of elementary theorems of basic linear algebra will be covered. The course is intended for majors in mathematics, engineering, science, and related fields.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- prove basic results of linear algebra, using appropriate proof-writing techniques.
- solve linear systems using matrices and matrix operations.
- utilize abstract concepts such as Euclidian n-space, multidimensional vector spaces, subspaces of vector spaces, and the relationship between matrices and n-tuples.
- analyze relationships between systems of equations, matrices, determinants, inverse matrices, vectors, linear transformations, row space, column space, null space, kernel, eigenvalues, and eigenvectors in linear algebra problems.
- analyze properties of inner product spaces and orthogonality and use them in applications

### MATH 420 Differential Equations

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 401 with a grade of "C" or better
- Advisory:MATH 410 with a grade of "C" or better; strongly recommended
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 240
- Catalog Date:August 1, 2023

This course will cover the theory and applications of solutions to ordinary differential equations and systems of ordinary differential equations. Students will be introduced to various topics useful in the solution of these differential equations including power series, Laplace transforms, matrices, eigenvalues and eigenvectors, and numerical methods.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- solve a variety of ordinary differential equations using techniques such as reduction of order, method of undetermined coefficients, variation of parameters, power series, and Laplace transforms.
- perform qualitative analysis on first-order equations using directions fields and phase portraits
- analyze, model, and solve elementary applied science problems such as Newton's Law of Cooling, mixing, falling bodies, spring/mass systems, and Newton's Second Law of Motion with ordinary differential equations.
- identify differential equations such as linear, separable, exact, and Cauchy-Euler.
- solve systems of linear differential equations.
- apply numerical techniques (Euler's method, modified Euler's, RK4) to approximate solutions to first order equations

### MATH 494 Topics in Mathematics

- Units:0.5 - 4
- Hours:9 - 72 hours LEC
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:August 1, 2023

This course provides the ability to take a course in mathematics that covers topics that are not part of the regular curriculum. This course may only be taken once, even if course offerings cover different topics. UC transfer credit will be awarded only after the course has been evaluated by the enrolling UC campus. The units completed for this course cannot be counted towards the minimum 60 units required for UC admissions.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- demonstrate understanding of the mathematical concepts studied in the course.
- demonstrate competence in the mathematical skills studied in the course.

### MATH 495 Independent Studies in Mathematics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:August 1, 2023

An independent studies project involves an individual student or a small group of students in study, research, or activities beyond the regularly offered mathematics courses. UC transfer credit will be awarded only after the course has been evaluated by the enrolling UC campus. The units completed for this course cannot be counted towards the minimum 60 units required for UC admissions.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- design and discuss a proposal of study with a supervising mathematics instructor.
- demonstrate the ability to independently pursue a course of study or project in mathematics.
- demonstrate understanding of the mathematical concepts studied in the course.
- demonstrate competence in the mathematical skills studied in the course.

### MATH 499 Experimental Offering in Mathematics

- Units:0.5 - 4
- Prerequisite:None.
- Transferable:CSU; UC
- Catalog Date:August 1, 2023

This is the experimental courses description.

## Mathematics Support (MATHS) Courses

### MATHS 10 Guided Individualized Support for Mathematics

- Units:0.5 - 2
- Hours:27 - 108 hours LAB
- Prerequisite:None.
- Corequisite:The student must be enrolled in a course with math content. This course may be from, but not limited to, the following designators: MATH, STAT, CHEM, PHYS, ASTR, BUS, ECON, CISP.
- Catalog Date:August 1, 2023

This course is open to all students currently enrolled in any course that uses or teaches mathematical concepts. The course enables students to build and review math topics that are necessary for success in any level of MATH, STAT, or other course. Learning objectives and the course topics will be designed based on the needs of each individual student with the guidance and support from the instructor and student tutors. This course cannot replace any existing mathematics course, and successful completion of MATHS 10 currently does not satisfy any mathematics prerequisite. This course is graded Pass/No Pass. Credit is earned in one-half unit increments and is dependent on progress in the course and class participation. This is an open-entry/open-exit course which may be taken for a maximum of two units.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- utilize mathematical terminology and articulate mathematical concepts appropriate to the relevant area of study.
- employ mathematical skills appropriate to the relevant level and area of study.
- analyze a mathematical problem and apply an appropriate set of problem-solving skills.

### MATHS 20 Support for Intermediate Algebra

- Units:3
- Hours:54 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 120
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 120, Intermediate Algebra. Topics and homework assignments are often connected to the students' assignments in MATH 120. Students who completed this topic as MATHS 299 are not eligible to take this course. This course is graded as Pass/No Pass. This course was formerly known as MATHS 120.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
- use support mathematics skills to solve systems of equations and solve linear, polynomial, rational, and absolute value inequalities.
- use support mathematics skills to use the definition of a function to determine if a relation is a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
- use support mathematics skills to sketch the graphs of basic functions, quadratic functions, transformations of these functions, and conic sections.
- use support mathematics skills to apply algebraic methods when solving word problems.

### MATHS 33 Support for Introduction to College Algebra

- Units:2
- Hours:36 hours LEC
- Prerequisite:None.
- Corequisite:MATH 333
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 333: Introduction to College Algebra as well as affective domain skills. Topics and homework assignments are often connected to the students' assignments in MATH 333. The course includes applications of the concepts and skills covered. This course is graded as Pass/No Pass.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use mathematics support skills to analyze and investigate properties of functions.
- use mathematics support skills to synthesize results from the graphs and/or equations of functions.
- use mathematics support skills to solve and apply equations including rational, linear, absolute value, polynomial, exponential, and logarithmic equations.
- use mathematics support skills to solve linear and nonlinear systems of equations and inequalities.
- use mathematics support skills to use functions and other algebraic techniques to model real world applications.
- use mathematics support skills to demonstrate the relationship between functions and their inverses graphically and algebraically.
- use mathematics support skills to apply transformations to the graphs of functions.

### MATHS 40 Support for Calculus for Business and Economics

- Units:3
- Hours:54 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 340
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Calculus for Business and Economics (MATH 340). Topics and homework assignments are often connected to the students' assignments in MATH 340. The course includes applications of the concepts and skills covered. This course is graded as Pass/No Pass. Students who have taken this course as MATHS 299 are not eligible to take this course. This course was formerly known as MATHS 140.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to find the derivatives of polynomial, rational, exponential, and logarithmic functions.
- use support mathematics skills to find the derivatives of functions involving constants, sums, differences, products, quotients, and the chain rule.
- use support mathematics skills to sketch the graphs of functions using horizontal and vertical asymptotes, intercepts, first and second derivatives to determine intervals where the function is increasing and decreasing, maximum and minimum values, intervals of concavity, and points of inflection.
- use support mathematics skills to analyze the marginal cost, profit, and revenue when given the appropriate function.
- use support mathematics skills to determine maxima and minima in optimization problems using the derivative.
- use support mathematics skills to find rates of change and tangent lines.
- use support mathematics skills to analyze revenue, cost, and profit.
- use support mathematics skills to find definite and indefinite integrals when applying the general integral formulas, integration by substitution, and other integration techniques.
- use support mathematics skills in business and economics applications.

### MATHS 42 Support for Modern Business Mathematics

- Units:3
- Hours:54 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 342
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Modern Business Mathematics. Topics and homework assignments are often connected to the students' assignments in MATH 342. The course includes applications of the concepts and skills covered. Students who completed this topic as MATHS 299 are not eligible to take this course. This course is graded as Pass/No Pass. This course was formerly known as MATHS 142.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to analyze formulas, tables, graphs, and data sets in order to form conclusions or make predictions.
- use support mathematics skills to calculate both present and future values involving compound interest and annuities.
- use support mathematics skills to analyze applications of annuities involving loan amortization and sinking funds, applying necessary formulas.
- use support mathematics skills to identify and graph linear, quadratic, power, polynomial, exponential, and logarithmic functions.
- use support mathematics skills to formulate and apply exponential growth or decay functions pertaining to business applications.
- use support mathematics skills to evaluate rates of change for a variety of elementary functions and apply them to marginal analysis.
- use support mathematics skills to find and interpret optimum values related to business applications.
- use support mathematics skills to solve linear programming problems using a graphical approach.

### MATHS 70 Support for College Algebra for Calculus

- Units:3
- Hours:54 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 372
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 372: College Algebra for Calculus as well as affective domain skills. Topics and homework assignments are often connected to the students' assignments in MATH 372. The course includes applications of the concepts and skills covered. This course is graded as Pass/No Pass. This course was formerly known as MATHS 172.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use mathematics support skills to solve equations and inequalities and manipulate expressions.
- use mathematics support skills to solve systems of equations and inequalities.
- use mathematics support skills to demonstrate a deep understanding of functions and their properties.
- use mathematics support skills to demonstrate a deep understanding of inverse functions and their algebraic and graphical relationships to their parent functions.
- use mathematics support skills to graph a variety of curves (showing intercepts, asymptotes, vertices, etc.).
- use mathematics support skills to solve application problems by creating and using mathematical models that involve synthesis of course concepts.

### MATHS 71 Support for Trigonometry for Calculus

- Units:2
- Hours:36 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 373
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in MATH 373: Trigonometry for Calculus. Topics and homework assignments are often connected to the students' assignments in MATH 373. The course includes applications of the concepts and skills covered. This course is graded as Pass/No Pass. This course was formerly known as MATHS 173.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use mathematics support skills to apply trigonometric functions to the angles of a right triangle and arcs on the unit circle.
- use mathematics support skills to evaluate trigonometric functions of common angles (using both radian and degree measure) and inverse trigonometric functions.
- use mathematics support skills to recognize, apply, and prove trigonometric identities and solve trigonometric equations.
- use mathematics support skills to create and analyze graphs of trigonometric functions, inverse trigonometric functions, curves in parametric form, and curves in polar form. (Trigonometric function graphing will include changes in period, phase, and amplitude.)
- use mathematics support skills to convert between polar and rectangular coordinates and equations, compute and solve equations involving complex numbers in standard and trigonometric form, and use DeMoivre's Theorem to evaluate powers and roots of complex numbers.
- use mathematics support skills to apply trigonometric and algebraic concepts as problem-solving tools by modeling problems with appropriate equations, including use of the Laws of Sines and Cosines and vector applications with vectors represented in both (a, b) and ai+bj form.
- use mathematics support skills to prove simple mathematical facts.

### MATHS 95 Support for Introduction to Mathematical Ideas

- Units:2
- Hours:36 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 300
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Introduction to Mathematical Ideas. Topics and homework assignments are often connected to the students' assignments in MATH 300. Students who completed this topic as MATHS 299 are not eligible to take this course. This course is graded as Pass/No Pass. This course was formerly known as MATHS 100.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to analyze inferences and conjectures present in a variety of mathematical ideas and systems.
- use support mathematics skills to construct well written solutions to mathematical exercises.
- use support mathematics skills to apply critical thinking skills developed in studying a mathematical topic to issues that transcend mathematics.
- use support mathematics skills to research and demonstrate an understanding of and explain mathematical ideas that are at an appropriate skill level.

### MATHS 96 Support for Mathematical Discovery

- Units:2
- Hours:36 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:MATH 310
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Mathematical Discovery (MATH 310). Topics and homework assignments are often connected to the students' assignments in MATH 310. This course is graded as Pass/No Pass. This course was formerly known as MATHS 110.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to explain mathematical relationships inherent in problems and situations.
- use support mathematics skills to make conjectures about mathematical relationships and content.
- use support mathematics skills to prove or disprove conjectures about mathematical relationships and content.
- use support mathematics skills in developing an appreciation of mathematical relevance to every day life.
- use support mathematics skills to analyze documents directing the study of mathematics in American schools, as well as the strategies, procedures, and emphases advocated in those documents.

### MATHS 299 Experimental Offering in Mathematics Support

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is the experimental courses description.

### MATHS 499 Experimental Offering in Mathematics Support

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is the experimental courses description.

## Statistics (STAT) Courses

### STAT 10 Support for Introduction to Probability and Statistics

- Units:2
- Hours:36 hours LEC
- Prerequisite:Placement through the assessment process.
- Corequisite:STAT 300
- Catalog Date:August 1, 2023

This course provides intensive instruction and practice in the core mathematical skills, competencies, and concepts necessary for success in Introduction to Probability and Statistics (STAT 300). Students will engage in topics and assignments that include the application of concepts and skills that are often connected to the students' assignments in STAT 300. This course is graded as Pass/No Pass. This course was formerly known as STAT 110.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- use support mathematics skills to select, produce, and interpret appropriate graphical and numerical summaries of data.
- use support mathematics skills to distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
- use support mathematics skills to construct and interpret confidence intervals for various characteristics of a population.
- use support mathematics skills to utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
- use support mathematics skills to use correlation and regression to analyze relationships between two numerical variables (bivariate data).
- use support mathematics skills when utilizing technology to perform statistical tasks.
- use support mathematics skills when using appropriate statistical techniques to analyze and interpret applications of data from the real world.

### STAT 100 Pre-Statistics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 34 with a grade of "C" or better, or placement through the assessment process.
- Catalog Date:August 1, 2023

Students will prepare for transfer-level Statistics, by exploring topics including ratios, rates, and proportional reasoning; arithmetic with fractions, decimals and percents; evaluating expressions, solving equations, and analyzing formulas to understand statistical measures; use of linear and exponential functions to model bivariate data; graphical and numerical descriptive statistics for quantitative and categorical data. Note: This course is not intended for students who plan to take courses in science, computer information science, engineering, mathematics, physics, chemistry, or business and economics.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- modify and simplify linear expressions, solve linear equations and inequalities, and evaluate statistical formulas using the order of operations agreement.
- sketch the graphs of linear and exponential functions, and find equations of linear and exponential functions given two points on the line or curve, to represent relationships in quantitative data.
- construct, evaluate, and analyze algebraic and statistical models when solving everyday problems.

### STAT 299 Experimental Offering in Statistics

- Units:0.5 - 4
- Prerequisite:None.
- Catalog Date:August 1, 2023

This is the experimental courses description.

### STAT 300 Introduction to Probability and Statistics

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 109, MATH 120, MATH 124, or STAT 100 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 110
- Catalog Date:August 1, 2023

This course is an introduction to probability and statistics. Students will engage in elementary principles and applications of descriptive statistics, counting principles, elementary probability principles, probability distributions, estimation parameters, hypothesis testing, linear regression and correlation, and ANOVA. Students will utilize the application of technology for various statistical analysis.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- select, produce, and interpret appropriate graphical and numerical summaries of data.
- distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
- interpret and solve probability applications that relate to everyday life.
- construct and interpret confidence intervals for various characteristics of a population.
- utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
- use correlation and regression to analyze relationships between two numerical variables (bivariate data).
- utilize technology to perform statistical tasks.
- use appropriate statistical techniques to analyze and interpret applications of data from the real world.

### STAT 480 Introduction to Probability and Statistics - Honors

- Units:4
- Hours:72 hours LEC
- Prerequisite:MATH 109, MATH 120, MATH 124, or STAT 100 with a grade of "C" or better, or placement through the assessment process.
- Transferable:CSU; UC
- General Education:AA/AS Area II(b); CSU Area B4; Cal-GETC Area 2 (effective Fall 2025); IGETC Area 2
- C-ID:C-ID MATH 110
- Catalog Date:August 1, 2023

This course is an introduction to probability and statistics designed for students in the honors program. Topics include elementary principles and applications of descriptive statistics, counting principles, elementary probability principles, probability distributions, estimation of parameters, hypothesis testing, linear regression and correlation, and ANOVA. Students will utilize the application of technology for various statistical analysis. Scientific calculators with two-variable statistical capabilities may be required for this class. This honors section uses an intensive instructional methodology designed to challenge motivated students. Honors courses are open to students who demonstrate an ability to write carefully reasoned, well-organized essays of varying lengths, are prepared to make clear oral presentations in class, and are able to actively contribute to seminar discussions. Credit will be awarded for either STAT 480 or STAT 300, not both.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- select, produce, and interpret appropriate graphical and numerical summaries of data.
- distinguish between probability models appropriate to different chance events and calculate probabilities according to these methods.
- construct and interpret confidence intervals for various characteristics of a population.
- utilize the basic components of hypothesis testing by conducting various hypothesis tests and interpreting their results.
- use correlation and regression to analyze relationships between two numerical variables (bivariate data).
- utilize technology to perform statistical tasks.
- use appropriate statistical techniques to analyze and interpret applications of data from the real world.

### STAT 495 Independent Studies in Statistics

- Units:1 - 3
- Hours:54 - 162 hours LAB
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:August 1, 2023

An independent studies project involves an individual student or a small group of students in study, research, or activities beyond the regularly offered statistics courses. UC transfer credit will be awarded only after the course has been evaluated by the enrolling UC campus. The units completed for this course cannot be counted towards the minimum 60 units required for admissions.

#### Student Learning Outcomes

Upon completion of this course, the student will be able to:

- design and discuss a proposal of study with a supervising instructor.
- demonstrate the ability to independently pursue a course of study or project in statistics.
- prepare a final report or project incorporating results of study or activities.

### STAT 499 Experimental Offering in Statistics

- Units:0.5 - 4
- Prerequisite:None.
- Transferable:CSU
- Catalog Date:August 1, 2023

This is the experimental courses description.

## Faculty

## Programs and Majors

## Check Out Degree Planner

If you're interested in a transfer degree (AA-T or AS-T), then check out Degree Planner, a tool that helps you complete your degree efficiently by mapping out what courses to take and when to take them.

## Science, Math and Engineering

This program is part of the Science, Math and Engineering meta major.