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### MATH 0300 Basic Mathematics

Textbook:   Math 0300 Course Materials, Prepared by Cindi Bluhm (sold only in NVC bookstore)

Required Materials:  Loose leaf notebook paper, a 1 inch 3 ring binder, 7 dividers with tabs, pencils, and medium index cards

Catalog Description:  Topics include operations on fractions, decimals, and integers; order of operations; and appropriate applications.  Please be advised that in addition to this course, you must complete a mandatory laboratory component of 600 minutes.

Prerequisites:   Placement by Accuplacer Exam or THEA Exam.

Semester Credit Hours:   (3-3-0)

Course Outcomes:   After the successful completion of this course, you will be able to solve application problems using the following skills:

1. Perform basic arithmetic operations with integers, fractions, and decimals.
2. Find the perimeter and area of polygons and circles.
3. Evaluate and simplify expressions using the order of operations.
4. Simplify arithmetic expressions involving positive exponents.
5. Use proportions to solve percent problems.
6. Evaluate and Simplify Algebraic Expressions
7. Solve applied problems using skills developed in this course.

### MATH 0301 Introduction to Algebra

Textbook: Beginning and Intermediate Algebra: 1st Ed, McKenna & Kirk; Pearson.

ISBN10: 0201787377 or ISBN13: 9780201787375

Catalog Description:   Topics include natural number exponents; algebraic expressions; linear equations and inequalities; concepts of lines; and appropriate applications. Please be advised that in addition to this course, you must complete a mandatory laboratory component of 600 minutes.

Prerequisites:   A grade of “C” or better in MATH 0300 or placement by Accuplacer Exam or THEA Exam.

Semester Credit Hours:   (3-3-0)

Course Outcomes:   After the successful completion of this course, you will be able to solve application problems using the following skills:

1. Perform operations on fractions and signed numbers.
2. Simplify algebraic expressions.
3. Solve linear equations and inequalities.
4. Solve literal equations for one variable.
5. Graph linear equations using (a) slope-intercept form, y = mx + b and (b) by finding x- and y-intercepts. Solve applied problems using skills developed in this course.

### MATH 0302 Elementary Algebra

Textbook: Beginning and Intermediate Algebra: 1st Ed , McKenna & Kirk; Pearson.

ISBN10: 0201787377 or ISBN13: 9780201787375

Catalog Description:   Topics include integer exponents; polynomials; factoring; rational expressions; rational equations; and appropriate applications.  Please be advised that in addition to this course, you must complete a mandatory laboratory component of 600 minutes.

Prerequisites:   A grade of “C” or better in MATH 0301 or placement by Accuplacer Exam or THEA Exam.

Semester Credit Hours:    (3-3-0)

Course Outcomes:   After the successful completion of this course, you will be able to solve application problems using the following skills:

1. Factor polynomials.
2. Perform arithmetic operations with polynomials.
3. Perform operations with rules of exponents.
4. Simplify rational expressions.
6. Perform arithmetic operations with rational expressions.
7. Solve applied problems using skills developed in this course.

### MATH 0303 Intermediate Algebra

Textbook:   Beginning and Intermediate Algebra: 1st Ed , McKenna & Kirk; Pearson.

ISBN10: 0201787377 or ISBN13: 9780201787375

Catalog Description:   Topics include rational exponents; radicals; linear and quadratic equations; linear systems; concepts of relations and functions; and appropriate applications.  Please be advised that in addition to this course, you must complete a mandatory laboratory component of 600 minutes.

Prerequisites:   A grade of “C” or better in MATH 0302 or placement by Accuplacer Exam or THEA Exam.

Semester Credit Hours:   (3-3-0)

Course Outcomes:   After the successful completion of this course, you will be able to solve application problems using the following skills:

1. Simplify and operate on complex numbers.
2. Solve quadratic equations by factoring, taking square roots, completing the square, and using the quadratic formula.
3. Simplify and operate on radical and rational expressions.
4. Solve equations involving radicals and rational expressions.
5. Graph and interpret parabolas.
6. Review topics covered throughout the developmental math curriculum.
7.  Solve applied problems using skills developed in this course.

### MATH 0442 PreStats

Information will be posted as soon as the syllabus for the Spring 2013 semester is revised...

### MATH 1314 College Algebra (Non-Math Science Track)

Textbook:  College Algebra:  2nd Ed, Coburn; McGraw Hill.

ISBN:  978-0-07351941-8 or 978-0-07-746671-8

Catalog Description:  Topics include functions, including the algebra of functions, composites, graphs of polynomial and rational functions, inverse functions, logarithmic and exponential functions, systems of equations using Cramer's Rule, matrices and determinants, sequences and series.

Prerequisites:   A grade of “C” or better in MATH 0303 or placement by Accuplacer Exam or THEA Exam.  Other prerequisites include ENGL 0300 and READ 0302.

Semester Credit Hours:   (3-3-0)

Course Outcomes:   After successful completion of this course, you should be able to:

1. Find combinations, compositions, and inverses of functions.
2. Find the domain of a function given its algebraic or graphical form.
3. Solve and graph linear and second-degree equations.
4. Use linear transformations to graph functions or determine the function from its graph.
5. Graph polynomial and rational functions.
6. Solve inverse functions.
7. Graph exponential and logarithmic functions.
8. Solve systems of linear equations by substitution and elimination.
9. Solve applied problems using skills developed in this course, including applications involving percent, simple and compound interest, taxes, and mathematical modeling with emphasis on exponential growth and decay, logistics growth, and logarithmic models.

### MATH 1324 Math for Business I (Finite Math)

Textbook: College Mathematics for Business, Economics, Life Sciences, and Social Sciences, twelfth edition by Barnett, Ziegler, and Byleen; Pearson Prentice Hall, 2011.

Course Description: Topics will include linear equations, quadratic equations, functions and graphs, inequalities, simple and compound interest, annuities, linear programming, matrices, systems of linear equations, applications to management, economics, and business.

Prerequisites: A grade of "C" or better in MATH 0303 or placement by Accuplacer Exam or THEA Exam.  Other prerequisites include ENGL 0300 and READ 0302.

Credits:  (3-3-0)

Course Outcomes:  After the successful completion of this course, you will be able to solve application problems using the following skills:

1. Solve and graph linear equations and inequalities.
2. Evaluate and graph functions, including quadratic, exponential, and logarithmic functions.
3. Solve problems involving simple interest and compound interest, including, including interest compounded continuously.
4. Find future value and present value of an annuity.
5. Solve systems of linear equations.
6. Solve systems of linear inequalities in two variables.
7. Maximize and minimize expressions using the Simplex Method.
8. Solve applied problems using skills developed in this course.

Textbook: College Mathematics for Business, Economics, Life Sciences, and Social Sciences,

12th Edition by Barnett, Ziegler, and Byleen; 2011

Pearson Prentice Hall
ISBN: 0-321-6454-6

Catalog Description: Topics include limits, continuity, derivatives of algebraic functions, implicit differentiation, higher-order derivatives, extrema, logarithmic and exponential functions, and integrals. Emphasis is on applications to business.

Prerequisites: A grade of "C " or better in MATH 1324 (Finite Mathematics) or MATH 1314/MATH 1414 (College Algebra).

Credits:  (3-3-0)

Course Outcomes: After successful completion of this course, you will have acquired the skills to:

1. Find limits of functions.
2. Determine the limit at infinity.
3. Define the equations of tangent lines.
4. Find derivatives of polynomial, rational, and other functions.
5. Apply the chain rule.
6. Determine relative and absolute extrema.
7. Differentiate exponential and logarithmic functions.
8. Find simple indefinite integrals.
9. Use definite integrals to find areas.
10. Find marginal cost, marginal revenue, and marginal profit.

### MATH 1332 Contemporary Math I (Math for Liberal Arts)

Textbook:   Math for Liberal Arts, Math 1332, Fall 2012 Edition.   Available only at NVC Bookstore .  OR  Thinking Mathematically: 5th Ed, Blitzer; Pearson.

ISBN 0-321-64585-5

Catalog Description:   This course is designated for nonmathematics majors and nonscience majors who need three hours of mathematics for degree requirements.  The course includes topics from logic, algebra, trigonometry, and probability.

Prerequisites:   MATH 0302 with a grade of "C" or better, or equivalent.  Other prerequisites include ENGL 0300 and READ 0302.

Semester Credit Hours:  (3-3-0)

Course Objectives:   With emphasis on the bolded items, the student will be able to:

1. Exhibit an understanding of elementary, intuitive set theory, including the concepts of subset, union, intersection, and cardinal number
2. Develop symbolic truth tables
3. Change numbers from base ten to other bases and vice versa
4. Exhibit facility with solving problems with the calculator, including integer problems, decimal problems, and percent problems
5. Convert within the metric system and between the metric system and the U.S. customary system
6. Solve elementary linear programming problems
7. Exhibit an understanding of elementary probability
8. Compute the mean, median, mode and standard deviation of a distribution
9. Use the normal curve to solve elementary problems in statistics
10. Calculate simple and compound interest
11. Find the sum of arithmetic and geometric series

### MATH 1350 Fundamentals of Mathematics for Teachers I

Textbook:  Mathematical Reasoning for Elementary Teachers (Authors: Long, DeTemple, Millman) 6th ed. ISBN-13: 978-0-321-71718-4 ISBN-10: 0-321-71718-X

Required Materials: course packet, a 2 inch 3-ring D binder, reinforcements, loose-leaf paper, pencils, 10 plastic pocket dividers

Catalog Description: Topics include sets, functions, numeration systems, number theory, and properties of the natural numbers, integers, rational, and real number systems. The emphasis is conceptual understanding, problem solving, and critical thinking. This course is designed specifically for students seeking teacher certification through grade 8.

Prerequisites:  MATH 1314 (College Algebra) with a grade of "C" or better, or equivalent.

Semester Credit Hours:   (3-3-0)

Course Outcomes:   After successful completion of this course, you should be able to:

1. Use various techniques in problem solving.
2. Use inductive and deductive reasoning in problem solving.
3. Recognize different types of sets and use Venn diagrams in problem solving.
4. Use algebra and function notation in problem solving.
5. Perform operations using different numeration systems.
6. Perform operations using alternative methods.
7. Use divisibility rules in factoring.
8. Use prime and composite numbers in finding GCF and LCM.
9. Perform operations using integers, decimals, and fractions.
10. Order integers, fractions, and decimals.
11. Solve applied problems using skills developed in this course.

### MATH 1351 Fundamentals of Mathematics for Teachers II

Textbook:  Mathematical Reasoning for Elementary Teachers (Authors: Long, DeTemple, Millman) 6th ed. ISBN-13: 978-0-321-71718-4 ISBN-10: 0-321-71718-X

Required Materials: course packet, a 2 inch 3-ring binder, reinforcements, loose-leaf paper, pencils, 10 plastic pocket dividers

Catalog Description: Topics include geometry, measurement, algebraic properties, data representation, probability, and statistics. The emphasis is conceptual understanding, problem solving, and critical thinking. This course is designed specifically for students seeking teacher certification through grade 8.

Prerequisites:  MATH 1350 with a grade of "C" or better, or equivalent.

Semester Credit Hours:   (3-3-0)

Course Outcomes:  After successful completion of this course, you should be able to:

1. Solve problems using ratio, proportions, and percents.
2. Represent and interpret data.
3. Use and interpret measures of central tendency and dispersion.
4. Use counting techniques and interpret measures of chance.
5. Use the basic ideas of geometry to recognize and to examine two and three-dimensional figures.
6. Work problems using transformations, tessellations, similarity, and topology.
7. Use different systems of measurement and convert from one to another.
8. Work problems concerning perimeter and area.
9. Work problems concerning surface area and volume.
10. Solve problems using the Pythagorean Theorem.
11. Solve applied problems using the skills developed in this course.

### MATH 1414 College Algebra (Math/Science Track)

Textbook:   College Algebra and Trigonometry:  2nd Ed, Ratti & McWaters;  Pearson Addison Wesley.

ISBN: 0-321-64471-9

Catalog Description:  This course includes the study of quadratics; polynomial, rational, logarithmic, and exponential functions; systems of equations; progressions; sequences and series; and matrices and determinants.

Prerequisites:   A grade of “C” or better in MATH 0303 or placement by Accuplacer ExamOther prerequisites include ENGL 0300 and READ 0302.

Semester Credit Hours:   (4-4-0)

Course Outcomes:   After successful completion of this course, you should be able to:

1. Review exponents, dimensional analysis, factoring, and simplifying rational expressions.
2. Find combinations, compositions, and inverses of functions.
3. Find the domain of a function given its algebraic or graphical form.
4. Solve and graph linear and second-degree equations.
5. Use linear transformations to graph functions or determine the function from its graph.
6. Solve and graph polynomial and rational functions.
7. Solve and graph exponential and logarithmic functions.
8. Solve application problems covering simple interest, taxes, exponential growth and decay models, logistics growth, logarithmic models, etc.
9. Solve systems of linear equations by substitution, elimination, and matrices.
10. Perform algebraic operations on matrices and find the inverse and determinant of a matrix.

### MATH 1442 Elementary Statistical Methods

Textbook:  Essentials of Statistics, 4th ed. by Mario F. Triola, Pearson Education, Inc.

ISBN:  0-321-64149-3

Catalog Description:   This course is a non-calculus introduction to statistics. Topics include the presentation and interpretation of data (using histograms and other charts, measures of location and dispersion, and exploratory data analysis), elementary probability and probability distribution functions (binomial, normal, t, chi-square), confidence intervals, hypothesis testing, correlation and linear regression, analysis of variance, and the use of statistical software.

Prerequisites:   A grade of “C” or better in MATH 0303 or MATH 0442 or placement by Accuplacer Exam.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:   (4-4-0)

Course Outcomes:   This course will prepare the student to better understand a world ruled by statistics including their utility possible bias. For students whose curriculum includes data analysis, this course will provide the groundwork for experimental design and analysis. This course is to provide the student with an understanding of statistical concepts and problem-solving methods for use in his/her chosen field or in further mathematics studies. The goals of the course will be achieved by the following course outcomes. After the successful completion of this course, you will be able to do the following skills:

1. To read and be able to critically interpret scientific statistical information.
2. Be able to organize and present data in a variety of formats.
3. Understand the fundamentals of probability.
4. Understand measures of central tendencies and dispersion.
5. Interpret the standard normal, binomial, and student t distribution tables.
6. Sampling and making inferences about populations using distributions is the fundamental goal of this course.  Distributions used will include the binomial, uniform, student t, and the normal.
7. Construct confidence intervals and interpret the probability of a true population mean falling within an interval.
8. Design and test hypotheses based on the normal sampling and proportional sampling.
9. An introduction to linear correlations and regressions.

### MATH 2318 Linear Algebra

Textbook:  Linear Algebra and Its Applications, 4th Edition by David C. Lay Pearson/ Addison Wesley, 2005
ISBN: 0321385179

Catalog Description: Topics include systems of linear equations, matrices and matrix operations, determinants, vectors and
vector spaces, inner products, change of bases, linear transformations, eigenvalues and eigenvectors

Prerequisites:  MATH 2413 with a grade of “C” or better, or equivalent.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:  (3-3-0)

Course Outcomes: After successful completion of this course, the student should be able to:

1. Solve a linear system using row operations and augmented matrices.
2. Find linear combinations of vectors.
3. Solve matrix equations.
4. Determine linear dependence and independence.
5. Find images of linear transformations.
6. Perform matrix operations.
7. Find the inverse of a matrix.
8. Determine which matrices are invertible.
9. Compute determinants.
10. Determine vector spaces and vector subspaces.
11. Find a basis for a space.
12. Find a coordinate vector related to a given base.
13. Find a basis and the dimension of a vector space.
14. Find the rank of a matrix.
15. Find the eigenvalues and eigenvectors of a matrix.
16. Find the characteristic equation of a square matrix.
17. Diagonalize a given matrix.
18. Find inner products, lengths, and orthogonality of vectors.
19. Find an orthogonal projection of one vector onto a span.
20. Find a Least-Squares solution of a matrix equation.

### MATH 2320 Differential Equations

(This course is only offered on the basis of need and at the discretion of the department.  Refer to your transfer institution to see if this course will count.)

Textbook: (At discretion of instructor)

Catalog Description: Ordinary differential equations, including linear equations, systems of equations, equations with variable coefficients, existence and uniqueness of solutions, series solutions, singular points, transform methods, and boundary value problems; application of differential equations to real-world problems.

Prerequisites:  MATH 2414 with a grade of "C" or better, or equivalent.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:  (3-3-0)

Course Objectives:

### MATH 2412 Precalculus

Textbook : College Algebra and Trigonometry 2nd ed. By Ratti/McWaters  ISBN: 978-0-321-64471-8

Catalog Description: This course applies algebra and trigonometry to the study of polynomial, rational, exponential, logarithmic, and trigonometric functions and their graphs. Also included are conic sections; circular and trigonometric functions, inverse circular functions, identities, conditional equations, graphs, solution of triangles, polar coordinates, complex numbers, and vectors; and mathematical induction.

Prerequisites:  MATH 1314 or MATH 1414 with a grade of “C” or better, or permission by department.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:  (4-4-0)

Course Outcomes:  After successful completion of this course, you should be able to solve problems using the following skills:

1. Exhibit an understanding of second degree relations, functions, and graphs.
2. Decompose expressions using partial fractions.
3. Exhibit an understanding of functions and their graphs, including conic sections and polynomial, exponential, and logarithmic functions.
4. Determine composites and inverses of functions.
5. Solve exponential and logarithmic equations.
6. Determine the values of trigonometric functions, including those involving special angles and right triangles.
7. Graph trigonometric functions; illustrate wavelength and phase shift.
8. Solve problems involving trigonometric identities and equations.
9. Solve problems involving the Law of Sines and the Law of Cosines.
10. Solve introductory problems involving vectors in the plane and polar coordinates.
11. Solve applied problems using skills developed in this course.

### MATH 2413 Calculus I

Textbook: Essential Calculus: Early Transcendentals, 2nd Edition James Stewart McMaster University

ISBN-10: 1133112285   ISBN-13: 9781133112280

Catalog Description: This course includes limits, continuity, derivatives and integrals of algebraic, transcendental, and inverse trigonometric functions, implicit differentiation and higher order derivatives, related rates, Rolle’s theorem, mean value theorem, velocity, acceleration, curve sketching and other applications of the derivative, indeterminate forms and L’Hopital’s rule, area, Riemann sums, and the fundamental theorems of calculus.

Prerequisites: MATH 1316 or MATH 2412 with a grade of “C” or better, or equivalent or permission by department.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:  (4-4-0)

Course Objectives: After successful completion of this course, you will be able to:

1. Exhibit a thorough understanding of functions.
2. Express the continuity of a function in terms of limits.
3. Determine equations of tangent lines.
4. Understand the concept of the derivative of a function.
5. Find derivatives using the power, product and quotient rules.
6. Find derivatives of trigonometric functions.
7. Find derivatives using the Chain Rule and generalized power rule.
8. Find higher-order derivatives.
9. Find derivatives of implicit functions.
10. Solve applied problems, including those involving related rates.
11. Find derivatives of exponential and logarithmic functions.
12. Evaluate indeterminate forms using L'Hospital's Rule.
13. Determine critical numbers, Maximum & minimum values, and inflection points.
14. Understand the implications of the Mean Value Theorem.
15. Exhibit facility sketching curves.
16. Solve optimization problems.
17. Solve other applied problems using skills developed in this course.

### MATH 2414 Calculus II

Textbook: Essential Calculus: Early Transcendentals, 2nd Edition James Stewart McMaster University

ISBN-10: 1133112285  ISBN-13: 9781133112280

Catalog Description:  This course includes areas between curves, volumes, arc length, surface area of a solid of revolution and other applications of integration, techniques of integration, numerical integration, improper integrals, parametric equations, derivatives, areas, and lengths in polar coordinates, sequences, and series.

Prerequisites:  MATH 2413 with a grade of "C" or better, or equivalent.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours: 4 - 4 - 0

Course Objectives:  The student should be able to solve problems involving:

1. Sum, product, quotient, chain, and power rules; implicit differentiation,
2. Maxima, minima, extrema, points of inflection, curve sketching,
3. Limit points, limits of functions, one-sided and infinite limits, and continuity,
4. Derivatives and integrals involving trigonometric functions,
5. Derivatives, integrals, and applications involving logarithmic and exponential functions,
6. Derivatives and integrals involving inverse trigonometric functions,
7. Indeterminate forms and L'Hospital's Rule,
8. Methods of integration (formulas, substitutions, trigonometric substitutions,
9. Arc length, volumes, and surface areas of solids of revolution,
10. Conic sections,
11. Parametric equations and derivatives,
12. Polar coordinates and graphs, polar-rectangular relationships, derivatives and areas in polar coordinates, and
13. Sequences and series, comparison, limit comparison ratio, and integral tests.

### MATH 2415 Calculus III

Textbook:  Essential Calculus: Early Transcendentals, 2nd Edition James Stewart McMaster University

ISBN-10: 1133112285  ISBN-13: 9781133112280

Catalog Description:  This course includes vector calculus, vector-valued functions, tangents to curves, velocity vector, curl, partial derivatives, chain rule, gradients, implicit functions, extrema of functions of several variables, multiple integrals including change of order and applications, surface integrals, and path independent line integrals.

Prerequisites: MATH 2414 with a grade of “C” or better, or equivalent.  Other prerequisites include ENGL 0301 and READ 0303.

Semester Credit Hours:  (4-4-0)

Course Objectives: The student should be able to develop a conceptual understanding of the fundamental ideas underlying geometry in the space and vectors, derivatives of functions of two or more variables, multiple integrals and vector calculus.

Topics:
Introduction/3D Coordinate Systems
Vectors & Vector Algebra
Lines & Planes
Vector Functions & Space Curves
Functions of Several Variables/Partial Derivatives
The Chain Rule
Directional Derivatives & The Gradient Vector
Maximum and Minimum Values & Lagrange Multipliers
Double Integrals/ Applications of Double Integrals
Triple Integrals/Applications of Triple Integrals
Change of Variables in Multiple Integrals
Vector Calculus/Line Integrals
Green’s Theorem, Curl & Gauss’s Divergence Theorem
Green’s Theorem, Curl & Gauss’s Divergence Theorem
Parametric Surfaces, Surface Integrals & Stoke’s Theorem

## Math Area Contacts

Tori Martinez
Phone: (210) 486-4298
Email: vmartinez420@alamo.edu
Office: JH-213

Yvette Uresti