# ASSOCIATE IN SCIENCE FOR TRANSFER (AS-T)

## Mathematics (M031007H)

The Associate in Science for Transfer in Mathematics Degree provides the lower-division mathematics course requirements to all students who are planning on transferring to a California State University (CSU) or other four-year university and major- ing in mathematics, physics, engineering, or computer science.

Program Learning Outcomes – Upon completion, students will be able to:

**Demonstrate knowledge of the fundamental mathematical principles.**

### Required Core:

- MATH 261† Calculus I 5 units
- MATH 262† Calculus II 5 units
- MATH 263† Calculus III 5 units

### List A: Select one (1) course:

- MATH 270† Linear Algebra 3 units
- MATH 275† Ordinary Differential Equations 3 units

### List B: Select one (1) course:

- CS 114† Programming in C
- or CS 216† Object-Oriented Programming in C ++
- MATH 227 Statistics
- or MATH 227S Statistics with Support
- or STAT 101 Statistics for the Social Sciences
- or Any List A course not already used.

Total = 21 - 22 units

† This course has a prerequisite or corequisite.

NOTE:* A minimum of 60 units and a cumulative GPA of 2.0 or higher must be completed to earn the Associate Degree. Major courses must each be completed with a grade of C or better. Always consult a counselor for information on program and graduation requirements, residency requirements and transfer information.*

# Mathematics Courses We Offer:

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 3 hours.

(NDA) - 3 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

Problem Set

Solutions

#### Course Description:

A review of elementary arithmetic. Topics include whole numbers, fractions, decimals, percent, measurements (including the metric system), and an introduction to elementary algebra.

#### Student Learning Outcomes:

- Utilize numbers and arithmetical operations efficiently and adaptively.
- Solve application problems involving arithmetic operations.
- Describe and analyze mathematically the spatial features of objects.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 4 hours. (NDA) - 4 UNITS

#### Course Description:

Course includes the following topics: graphical techniques; probability and probability distributions; sampling; estimation; correlations; regression; hypotheses testing; categorical data. Emphasis is on data analysis and interpretation, using sample data to extrapolate population characteristics.

#### Student Learning Outcomes:

- Critically analyze descriptive statistics by reading charts, graphs and results of statistical analyses.
- Choose the appropriate technique, and use technology to perform the necessary calculations for statistical analyses.
- Interpret results of inferential statistical calculations for Confidence Intervals, Hypothesis Testing, and Regression Analysis.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 4 hours, Lab: 1 hour.

(NDA) - 4 UNITS

#### Course Description:

Course includes the following topics: graphical techniques; probability and probability distributions; sampling; estimation; correlations; regression; hypotheses testing; categorical data. Emphasis is on data analysis and interpretation, using sample data to extrapolate population characteristics.

#### Student Learning Outcomes:

- Critically analyze descriptive statistics by reading charts, graphs and results of statistical analyses.
- Choose the appropriate technique, and use technology to perform the necessary calculations for statistical analyses.
- Interpret results of inferential statistical calculations for Confidence Intervals, Hypothesis Testing, and Regression Analysis.

##### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

3 units (Lecture: 3 hours | Lab: 1 hour)

##### Course Description:

Math 230 is an introduction to the spirit and style of mathematics and its pursuit as a human endeavor. Topics are chosen from a variety of mathematical fields including logic, set theory, systems of numeration, number theory, algebra, the metric system, geometry, mathematical systems, consumer mathematics, probability, statistics, graph theory, voting and apportionment which are intended to illustrate the nature of mathematical discovery, the utility of mathematical applications, and the beauty of geometrical design.

##### SLOs:

- Use the methods discussed in the course to analyze information and solve real-life mathematical problems.
- Understand the principles of borrowing and saving to compare different financial opportunities and make informed decisions.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 5 hours.

5 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

#### Course Description:

Course includes the following topics and their business applications: polynomial, exponential and logarithmic functions; differentiation and integration; integration by parts; numerical integration; improper integrals; multivariable calculus.

#### Student Learning Outcomes:

Apply the techniques of calculus to solve business-related problems.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 3 hours.

(NDA) - 3 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

#### Course Description:

This course studies the trigonometric functions, including their values, graphs, inverses, and verifying identities. It also includes solving right triangles and others, radian measure and polar equations.

#### Student Learning Outcomes:

- Examine and interpret the graphs of basic trigonometric functions and their transformation.
- Apply concepts of trigonometry to solve problems involving trigonometric functions.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 3 hours, Lab: 1 hour. (NDA) - 3 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

#### Course Description:

Introduces trigonometric functions, their graphs, inverses, and fundamental identities. Trigonometric equations are solved. The laws of sines and cosines; vectors; scalar and vector products are introduced. Polar coordinates and equations are introduced and used to represent complex numbers.

#### Student Learning Outcomes:

- Examine and interpret the graphs of basic trigonometric functions and their transformation.
- Apply concepts of trigonometry to solve problems involving trigonometric functions.

#### Prerequisite:

Intermediate algebra, the equivalent or higher, completed at the secondary or post-secondary level; or by meeting CA Title 5 CCR § 55063 math competency requirement of intermediate algebra, per LACCDAP4100; or by placing into any college-level math course.

Lecture: 3 hours.

(NDA) - 3 UNITS

#### Entry Skills:

Solutions

If you are unable to correctly answer the questions in the above problem sets, you are strongly advised to take Math 125 (Intermediate Algebra) or Math 134 (Accelerated Elementary and Intermediate Algebra).

#### Course Description:

The properties of real numbers, relations, functions and their graphs, matrices and determinants, complex numbers, theory of equations, permutations, combinations, and probability.

#### Student Learning Outcomes:

- Solve and/or graph higher order equations, functions, systems of equations and inequalities.
- Calculate sums and terms of sequences and series.

Lecture: 3 hours | Lab: 2 hours

First semester of an applied course in calculus for biological and other life-sciences. Topics include functions of one variable, graphs, limits, continuity, derivatives, techniques for finding maxima/minima, introduction to integration, fundamental theorem of calculus and integration by substitution.

Prerequisite: MATH 240 or MATH 240S and MATH 245 or MATH 260

Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

Problem Set

#### SLOs:

- Represent, understand and explain mathematical information symbolically, graphically, numerically and verbally.
- Develop mathematical models of real-world situations and explain the assumptions and limitations of those models.
- Use models to make predictions, draw conclusions, check whether the results are reasonable, and find optimal results using technology when necessary and appropriate.

Lecture: 3 hours Lab: 2 hours

#### Prerequisite:

MATH 247 or MATH 261

Math 248 is the second semester of an applied calculus course sequence for biological and other life-sciences. Topics include techniques of integration, introduction to differential equations, applications of calculus in probability, elements of multivariable calculus and linear algebra.

#### SLOs

- Understand and explain applications of integration techniques;
- Develop mathematical models of real-world situations and explain the assumptions and limitations of those models;
- Use models to make predictions, draw conclusions, check whether the results are reasonable, and find optimal results using technology when necessary and appropriate.

#### Prerequisite:

Math 240 or appropriate skill level demonstrated through the Math assessment process.

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

Problem Set

#### Course Description:

Consists of topics essential for a comprehensive background for the calculus sequence. Topics include functional analysis, analytic geometry, theory of equations, induction, sequences and series, trigonometry and polar coordinates.

#### Student Learning Outcomes:

- Manipulate and simplify algebraic and trigonometric expressions and equations common in a Calculus course.
- Graph and analyze various functions common in a calculus course.

#### Prerequisite:

Math 240 and 245 or 260 or appropriate skill level demonstrated through the Math assessment process.

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Entry Skills:

Enrollment in this class assumes knowledge of some algebraic skills. Bellow you can find a sample of skills that that traditionally have contributed to the likelihood of success.

Problem Set

Solutions

The content of the worksheets are covered in the pre-requisite courses: Math 245 (College Algebra) or Math 240 (Trigonometry) and Math 260 (Pre-calculus).

#### Course Description:

First course of calculus and includes functions, limits, derivatives and their applications, differentials, integrals and their applications.

#### Student Learning Outcomes:

- Determine and analyze limits and derivatives as appropriate to single variable calculus.
- Evaluate and interpret integrals as appropriate to single variable calculus.

#### Prerequisite:

Math 261 (previously Math 265).

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Course Description:

Second course of calculus. Includes differentiation and integration of transcendental functions, polar coordinates, specialized methods of integration, parametric equations, and infinite series.

#### Student Learning Outcomes:

- Demonstrate proficiency in evaluating integrals using various techniques of integration.
- Determine convergence/divergence of sequences and series.

#### Prerequisite:

Math 262 (previously Math 266).

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Course Description:

This course of calculus, includes solid analytic geometry, partial differentiation, multiple integration, vector analysis, infinite series and an introduction to differential equations.

#### Student Learning Outcomes:

- Analyze vectors and surfaces in three dimensions geometrically and algebraically.
- Apply the concepts of differentiation and integration of functions to solve multivariable calculus problems.

#### Prerequisite:

Math 262.

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Course Description:

Covers vector spaces, linear transformation, matrices, matrix algebra, determinants, Eigen vectors and Eigen values.

#### Student Learning Outcomes:

- Solve a system of linear equations using matrix methods.
- Apply results from solutions of systems to questions of basis, dimension, and linear independence in vector spaces.

Lecture: 5 hours

#### Prerequisite:

MATH 262 and CS 112 or CS 113 or CS 116 or CS 119 |

Introduction to the discrete structures used in Computer Science. Topics include sets, relations, functions and logic along with formal methods of proof such as contradiction, contrapositive, induction, diagonalization, recursion, and the Pigeonhole principle. These ideas and methods are developed by writing programs to solve problems from combinatorics and counting, elementary number theory, and graph theory. Topics from map coloring, complexity, and cryptography are also discussed.

#### Student Learning Outcomes:

- Demonstrate the ability to solve problems using counting techniques and combinatorics in the context of discrete probability.
- Utilize discrete structures such as sets, functions, relations, and sequences to construct, and analyze algorithms, and implement the latter in a programming language.
- Demonstrate mathematical claims by constructing proofs using direct proof, proof by contraposition, proof by contradiction, proof by cases, mathematical induction, and recursive definition.

#### Prerequisite:

Math 262.

Lecture: 5 hours.

(NDA) - 5 UNITS

#### Course Description:

First and higher linear equations are treated completely including techniques of exactness, separation of variables; special cases of nonlinear equations are investigated.

#### Student Learning Outcomes:

- Formulate an appropriate differential equation to model and solve applied problems using various methods.
- Solve higher-order constant-coefficient linear differential equations and systems of differential equations using various methods.