MATH Mathematics-Nursing. MATH Remedial Mathematics I-Business & Economics. MATH Remedial Mathematics II-Business and Economics

Size: px
Start display at page:

Download "MATH Mathematics-Nursing. MATH Remedial Mathematics I-Business & Economics. MATH Remedial Mathematics II-Business and Economics"

Transcription

1 MATH Mathematics-Nursing MATH Remedial Mathematics I-Business & Economics MATH Remedial Mathematics II-Business and Economics MATH Remedial Mathematics I-Science (3 CH) MATH Remedial Mathematics II-Science MATH Mathematics-Business & Economics MATH Remedial Mathematics II-Business & Economics MATH General Applied Mathematics (3 CH) MATH Calculus I (3 CH) Limits and continuity. Differentiation. Applications of derivatives. Integration. Inverse functions. Applications of the integral. MATH Calculus II (3 CH) Transcendental functions. Techniques of integration. Sequences and infinite series. Parametric equations and polar coordinates MATH General Mathematics I (4 CH) MATH General Mathematics II (2 CH) MATH Mathematics I - Biology (3 CH) MATH Mathematics I-Business and Economics (3 CH) MATH Business Mathematics I (3 CH) Algebra Review. Equations: Linear, fractional, quadratic and radical equations. factorizing higher degree equations. Functions and Graphs: Functions. Domain. Evaluating a function. Combinations and composition of functions. Graphs of functions in rectangular coordinates. Lines, Parabolas and Systems: Equations of lines. Parallel and perpendicular lines. Graphing quadratic functions. Sys-tems of linear equations with at most three variables. Exponential and Logarithmic Functions: Graph of exponential functions. Population growth. Graph of logarithmic functions. Solving logarithmic and exponential equations. Matrices: Transpose of a matrix. Special matrices. Matrix addition, subtraction, scalar multiplica-tion and multiplication. Reduction methods for homogeneous and nonhomogeneous systems. Differentiation: Derivatives. Tangent lines. Rules of differentiation. Chain rule. Derivatives of loga-rithmic and exponential functions. Implicit differentiation. Integration: Indefinite integrals. Basic integration formulas. MATH Mathematics and Quantitative Analysis (2 CH) MATH Mathematics I-Engineering (3 CH) MATH Mathematics I-Engineering (3 CH) MATH Mathematics II-Engineering (3 CH)

2 MATH Vector Calculus (3 CH) MATH Advanced Calculus (3 CH) MATH Mathematics II-Biology (3 CH) MATH Calculus III (3 CH) Vectors. Vector calculus. Functions of several variables. Differentials and applications. Double and triple integrals. MATH Calculus IV (3 CH) Line integrals. Surface integrals. Fourier series. Some special functions. Complex numbers. MATH Differential Equations (3 CH) First order differential equations. Second order differential equations. Linear systems of differential equations. Laplace transforms. Differential equations with variables coefficients. MATH Mathematics-Computer Science (3 CH) Infinite Series: Sequences of real numbers. Infinite series. Geometric series. The divergence test. The integral test. Comparison theorems. The root test. The ratio test. Alternating series. Ab-solute convergence. Alternating series test. Power series. Taylor and Maclaurin series. Fourier Series. Some Special Functions: Gamma function. Beta function. Error function. Applications. Functions of Several Variables: Elementary examples. Quadratic surfaces. Limits and Continuity. Direction angle. Differentials and Applications: Notion of differentiability. Differentials. Directional derivatives. Mean value theorem. Chain rules. Maximum and Minimum values. Lagrange s method. Double and Triple Integrals: Double integrals. Properties. Evaluation by repeated integrals. Polar coordinates. Triple integrals. Properties. Evaluation by repeated integrals. Cylindrical and spherical coordi-nates. Applications. Differential Equations: Classification by type. Classification by order. Linearity. Solutions. Initial value prob-lem. Separable variables. Homogeneous equations. Exact equations. Linear equations. Integrating factor. Homogeneous equations with constant coefficients. MATH Mathematics-Chemistry (3 CH) Logic, Sets and Functions: Logic. Propositional equivalences. Predicates and quantifiers. Sets. Set operations. Functions. Sequences and summations. Mathematical Reasoning: Methods of proof. Mathematical induction. Relations: Relation and their properties. N-ary relations and their applications. Representing rela-tions. Equivalence relations. Partial ordering. Counting: The basics of counting. The pigeonhole principle. Permutations and combinations. Ge-neralized permutations and combinations. Graphs: Introduction to graphs. Graph Terminology. Representing graphs and graphs isomor-phism. Connectivity. Euler and Hamiltonian paths. Planar graphsintroduction. MATH Mathematics-Engineering (3 CH) First-Order Differential Equations: Initial-value problem. separable variables. Homogeneous equations. Exact equations. Li-near equations. Integrating factor. Bernoulli equation. Applications. Second-Order Differential Equations: Initial-value and Boundary-value problems. Linear differential operators. Reduction of order. Homogeneous equations with constant coefficients. Nonhomogeneous equations. Method of undetermined coefficients. method of variation of parameters. some nonlinear equations. Ap-plications. Higher order Differential Equations. Laplace Transforms: Definitions. Properties. Inverse Laplace transforms. Solving initial-value problems. Special functions: Heavyside unit step function. Convolution theorem. System of Linear Differential Equations: Definitions. Elimination method. Application of Linear Algebra. Homogeneous linear systems. Nonhomogeneous linear systems. Solving systems by Laplace transforms. Series Solutions: Cauchy-Euler equation method. Solutions about ordinary points. Solutions about singular points. Method of Frobenius. Second Solutions and Logarithm terms. Partial Differential Equations: Some mathematical models. Fourier series solutions. Method of seperation of variables. The D Alembert solution of the wave equation. Applications.

3 MATH Mathematics-Physics (3 CH) MATH Foundations of Mathematics (3 CH) Mathematical logic. Sets and families. Relations. Functions. Countable and uncountable sets. MATH Business Mathematics II (3 CH) This course covers some economic applications of mathematical concepts such as the linear and non linear functions, difference equations, partial derivatives, constrained and unconstrained optimization problems, definite and indefinite integration in addition to mathematics of finance. MATH Real Analysis (3 CH) Structure of point sets. Real numbers. Real sequences. Limits and continuity. Differentiation and mean value theorem. Riemann integral. Riemann-Stieltjes integral. MATH Linear Algebra (3 CH) of linear equations. Matrices and matrix operations. Determinants. Vector spaces. Linear transformations. Eigenvalues and eigenvectors. MATH Computational & Linear Algebra (3 CH) MATH Abstract Algebra (3 CH) Relations and applications. Binary operations and algebraic systems. Groups. Cosets. Introduction to rings and fields. MATH Discrete Mathematics (3 CH) General Applied Mathematics Sets, operation on sets, review of numbers (Natural, Integer, Rational, Irrational and Real numbers), prime numbers, divisibility, least common multiple, greatest common divisor. Logic, truth tables, connectives. Functions (polynomial, roots, rational, absolute value, exponential), some applications (profit simple and compound). Equations, inequalities, simple applications of equations, some linear programming problems (feasible solutions, blending model, production model, transportation). Analytic geometry: Cartesian coordinate system, distance between two points, midpoint formula, lines, circles. Matrices operations, determinant (3?3), solutions of systems of linear equations (Cramer s rules). Statistics: Frequency tables, Mean, Median, Mode, some application (grade point average). MATH Mathematics III-Engineering (3 CH) MATH Mathematics IV-Engineering (3 CH) MATH Partial Differential Equations (3 CH) First order partial differential equations. Second order partial differential equations. Elliptic partial differential equations. Parabolic partial differential equations. Hyperbolic partial differential equations. MATH Real Analysis II (3 CH) Euclidean n space Continuous functions Differentiable functions Implicit and inverse function theorems Maxima and minima. MATH Complex Analysis (3 CH) Review on complex numbers. Analytic functions. Elementary functions. Line integrals. Series. MATH Topology (3 CH) Basic concept. Basic topological constructions. Sequential convergence in topological space and derivatives sets. Basic topological properties.

4 MATH Linear Algebra II (3 CH) Linear transformation and matrices Diagonalization Inner. MATH Abstract Algebra II (3 CH) Normal subgroups Cyclic structure of finite permutation groups Direct product of groups Action of groups on sets Ideals and domains Euclidean domains Applications. MATH Number Theory (3 CH) ntegers. Greatest common divisor and prime factorization. Congruence. Application and some special congruence. Multiplicative functions. Primitive roots. Introduction to quadratic residues and reciprocity. MATH Modern Geometry (3 CH) Axiomatic systems. Finite geometries. Euclidean geometry. Neutral geometry. Hyperbolic geometry. MATH Programming and Scientific Computation I MATH Numerical Analysis I Errors in numerical computation. Solutions of nonlinear equations. Direct methods for solving linear systems. Interpolation and polynomials approximations. Numerical differentiation. Numerical integration. MATH Numerical Methods I MATH Operations Research I (3 CH) Overview of operations research. Linear programming. The transportation problem. MATH Graphic Theory & Appllication (3 CH) Introduction to graph. Paths and cycles. Trees. Planarity. Coloring graphs. MATH Advanced Mathematical Methods (3 CH) Some special functions. Method of eigenfunction expansions. Integral transforms. Integral equations. MATH Mathematics-Electrical Engineers MATH Advanced Mathematics (3 CH) Mathematics for Electrical Engineers. Complex Numbers and Complex Functions: Algebra of complex numbers. Modulus and argument. Trigonometric form. Exponen-tial form. Roots. De Moivre's theorem. Analytic Functions: Functions of a complex variable. Mappings. Limits. Continuity. Derivatives. Cauchy-Riemann equations. Polar coordinates. Analytic functions. Harmonic functions. Har-monic conjugate. Elementary functions. Complex Integration: Definite integrals. Contours. Line integrals (Real). Line integral (Complex). Cauchy in-tegral theorem. Cauchy integral formulas. Taylor's series and Laurent's series of ana-lytic functions. Residue theorem. Applications. Fourier Transforms: Fourier transforms. Properties. Inverse of the Fourier transform. Convolution theorem. Fourier sine and Fourier Cosine transforms. MATH Theory of Differential Equations (3 CH) Linear systems of differential equations. Nonlinear systems of differential equations. Stability of linear differential equations. MATH Theory of Distributions (3 CH) Space of test functions Space of distributions Tensor product and convolution Space of tempered distributions.

5 MATH Complex Analysis II (3 CH) Residue theory Mapping by elementary functions Conformal mapping Application of conformal mapping Further theories of functions. MATH Topology II (3 CH) Metric spaces as topological spaces sequential spaces Other topological properties. MATH Functional Analysis (3 CH) Linear spaces. Metric spaces. Normed spaces. Banach spaces. Linear operators and functionals. Inner product spaces. MATH Number Theory II (3 CH) Prime numbers and their distribution Dirichlet s series and Euler s products Further Diaphantine equations and elliptic curves Extension of the p-adic field Qp. MATH Applied Algebra (3 CH) Boolean algebra and switching circuits Introduction to formal languages and automata Polga enumeration Introduction to algebraic coding Introduction to cryptography. MATH Projective Geometry (3 CH) Finite projective geometry Plane projective geometry Projective transformation Projective, affine and Euclidean geometry. MATH Introduction to Differential Geometry (3 CH) Curves. Surfaces. Differentiability structure of regular surfaces. Orientability and isometries of regular surfaces. MATH Numerical Analysis II (3 CH) Iterative methods for solving linear systems. Approximation theory. Eigenvalues. Numerical solutions of the initial value problems. Numerical solutions of the boundary value problems. Numerical solutions of partial differential equations. MATH Numerical Methods II (3 CH) MATH Operations Research II (3 CH) Integer programming. Dynamic programming. Nonlinear programming. MATH Mathematical Modeling (3 CH) Difference equations (Dynamical system 1). Difference systems (Dynamical system 2). Differential equations (Dynamical system 3). Applications. MATH Theory of Elasticity (3 CH) Tensor calculus Analysis of stress Analysis of strain Field equations Elastostatic problems Thermoelasticity Theory of plates. MATH Fluid Dynamics (3 CH) MATH Topics in Principles of Mathematics (2 CH) MATH Independent Study This course aims at providing: depth in some branch of mathematics; skills of independent study and scientific report-

6 writing, and ability to use research tools and methods by accessing and using the library and data bases through modern information technology. MATH Special Topics (3 CH) This course usually aims at either pursuing in more depth the study of a certain discipline, or an opportunity for learning some advanced coherent topics, or exposure to new material in a currently active field of mathematics. MATH Senior Project (3 CH) This course aims at applying the educational experience gained, to study practical problems and issues, associated with realistic field, related to the nature of professional work and its requirements, and putting what a student has learned into practice, in order to reach solutions to problems, and procedural issues, from the perspective of global view.

Mean value theorem, Taylors Theorem, Maxima and Minima.

Mean value theorem, Taylors Theorem, Maxima and Minima. MA 001 Preparatory Mathematics I. Complex numbers as ordered pairs. Argand s diagram. Triangle inequality. De Moivre s Theorem. Algebra: Quadratic equations and express-ions. Permutations and Combinations.

More information

Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours

Mathematics (MAT) MAT 061 Basic Euclidean Geometry 3 Hours. MAT 051 Pre-Algebra 4 Hours MAT 051 Pre-Algebra Mathematics (MAT) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student must earn a grade of C or in order to enroll in MAT

More information

MATHEMATICS (MATH) 3. Provides experiences that enable graduates to find employment in sciencerelated

MATHEMATICS (MATH) 3. Provides experiences that enable graduates to find employment in sciencerelated 194 / Department of Natural Sciences and Mathematics MATHEMATICS (MATH) The Mathematics Program: 1. Provides challenging experiences in Mathematics, Physics, and Physical Science, which prepare graduates

More information

Sequence of Mathematics Courses

Sequence of Mathematics Courses Sequence of ematics Courses Where do I begin? Associates Degree and Non-transferable Courses (For math course below pre-algebra, see the Learning Skills section of the catalog) MATH M09 PRE-ALGEBRA 3 UNITS

More information

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

More information

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing! MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

More information

Math Course Descriptions & Student Learning Outcomes

Math Course Descriptions & Student Learning Outcomes Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate

More information

School of Mathematics, Computer Science and Engineering. Mathematics* Associate in Arts Degree COURSES, PROGRAMS AND MAJORS

School of Mathematics, Computer Science and Engineering. Mathematics* Associate in Arts Degree COURSES, PROGRAMS AND MAJORS Mathematics School of Mathematics, Computer Science and Engineering Dean: Lianna Zhao, MD Academic Chair: Miriam Castroconde Faculty: Miriam Castroconde; Terry Cheng; Howard Dachslager, PhD; Ilknur Erbas

More information

SCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA.

SCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA. Pocket book of Electrical Engineering Formulas Content 1. Elementary Algebra and Geometry 1. Fundamental Properties (real numbers) 1 2. Exponents 2 3. Fractional Exponents 2 4. Irrational Exponents 2 5.

More information

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu

Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu Mathematics INDIVIDUAL PROGRAM INFORMATION 2014 2015 866.Macomb1 (866.622.6621) www.macomb.edu Mathematics PROGRAM OPTIONS CREDENTIAL TITLE CREDIT HOURS REQUIRED NOTES Associate of Arts Mathematics 62

More information

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

More information

UNIVERSITY GRADUATE STUDIES PROGRAM SILLIMAN UNIVERSITY DUMAGUETE CITY. Master of Science in Mathematics

UNIVERSITY GRADUATE STUDIES PROGRAM SILLIMAN UNIVERSITY DUMAGUETE CITY. Master of Science in Mathematics 1 UNIVERSITY GRADUATE STUDIES PROGRAM SILLIMAN UNIVERSITY DUMAGUETE CITY Master of Science in Mathematics Introduction The Master of Science in Mathematics (MS Math) program is intended for students who

More information

Appendix 3 IB Diploma Programme Course Outlines

Appendix 3 IB Diploma Programme Course Outlines Appendix 3 IB Diploma Programme Course Outlines The following points should be addressed when preparing course outlines for each IB Diploma Programme subject to be taught. Please be sure to use IBO nomenclature

More information

MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS

MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS * Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices

More information

Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer

Mathematics. Mathematics MATHEMATICS. 298 2015-16 Sacramento City College Catalog. Degree: A.S. Mathematics AS-T Mathematics for Transfer MATH Degree: A.S. AS-T for Transfer Division of /Statistics & Engineering Anne E. Licciardi, Dean South Gym 220 916-558-2202 Associate in Science Degree Program Information The mathematics program provides

More information

PCHS ALGEBRA PLACEMENT TEST

PCHS ALGEBRA PLACEMENT TEST MATHEMATICS Students must pass all math courses with a C or better to advance to the next math level. Only classes passed with a C or better will count towards meeting college entrance requirements. If

More information

Higher Education Math Placement

Higher Education Math Placement Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

More information

Complex Function Theory. Second Edition. Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY

Complex Function Theory. Second Edition. Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY Complex Function Theory Second Edition Donald Sarason >AMS AMERICAN MATHEMATICAL SOCIETY Contents Preface to the Second Edition Preface to the First Edition ix xi Chapter I. Complex Numbers 1 1.1. Definition

More information

Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices. Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

More information

Essential Mathematics for Computer Graphics fast

Essential Mathematics for Computer Graphics fast John Vince Essential Mathematics for Computer Graphics fast Springer Contents 1. MATHEMATICS 1 Is mathematics difficult? 3 Who should read this book? 4 Aims and objectives of this book 4 Assumptions made

More information

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary) Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

More information

Credit Number Lecture Lab / Shop Clinic / Co-op Hours. MAC 224 Advanced CNC Milling 1 3 0 2. MAC 229 CNC Programming 2 0 0 2

Credit Number Lecture Lab / Shop Clinic / Co-op Hours. MAC 224 Advanced CNC Milling 1 3 0 2. MAC 229 CNC Programming 2 0 0 2 MAC 224 Advanced CNC Milling 1 3 0 2 This course covers advanced methods in setup and operation of CNC machining centers. Emphasis is placed on programming and production of complex parts. Upon completion,

More information

Please start the slide show from the beginning to use links. Click here for active links to various courses

Please start the slide show from the beginning to use links. Click here for active links to various courses Please start the slide show from the beginning to use links Click here for active links to various courses CLICK ON ANY COURSE BELOW TO SEE DESCRIPTION AND PREREQUISITES To see the course sequence chart

More information

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1 Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse

More information

Diablo Valley College Catalog 2014-2015

Diablo Valley College Catalog 2014-2015 Mathematics MATH Michael Norris, Interim Dean Math and Computer Science Division Math Building, Room 267 Possible career opportunities Mathematicians work in a variety of fields, among them statistics,

More information

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know

More information

Algebra and Geometry Review (61 topics, no due date)

Algebra and Geometry Review (61 topics, no due date) Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

More information

SEMESTER PLANS FOR MATH COURSES, FOR MAJORS OUTSIDE MATH.

SEMESTER PLANS FOR MATH COURSES, FOR MAJORS OUTSIDE MATH. SEMESTER PLANS FOR MATH COURSES, FOR MAJORS OUTSIDE MATH. CONTENTS: AP calculus credit and Math Placement levels. List of semester math courses. Student pathways through the semester math courses Transition

More information

BookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line

BookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina - Beaufort Lisa S. Yocco, Georgia Southern University

More information

PHILOSOPHY OF THE MATHEMATICS DEPARTMENT

PHILOSOPHY OF THE MATHEMATICS DEPARTMENT PHILOSOPHY OF THE MATHEMATICS DEPARTMENT The Lemont High School Mathematics Department believes that students should develop the following characteristics: Understanding of concepts and procedures Building

More information

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009

Prentice Hall Algebra 2 2011 Correlated to: Colorado P-12 Academic Standards for High School Mathematics, Adopted 12/2009 Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level

More information

MATH 132: CALCULUS II SYLLABUS

MATH 132: CALCULUS II SYLLABUS MATH 32: CALCULUS II SYLLABUS Prerequisites: Successful completion of Math 3 (or its equivalent elsewhere). Math 27 is normally not a sufficient prerequisite for Math 32. Required Text: Calculus: Early

More information

MATHEMATICAL SCIENCES, BACHELOR OF SCIENCE (B.S.) WITH A CONCENTRATION IN APPLIED MATHEMATICS

MATHEMATICAL SCIENCES, BACHELOR OF SCIENCE (B.S.) WITH A CONCENTRATION IN APPLIED MATHEMATICS VCU MATHEMATICAL SCIENCES, BACHELOR OF SCIENCE (B.S.) WITH A CONCENTRATION IN APPLIED MATHEMATICS The curriculum in mathematical sciences promotes understanding of the mathematical sciences and their structures,

More information

MATHEMATICS COURSES Grades 8-12 2015-2016

MATHEMATICS COURSES Grades 8-12 2015-2016 MATHEMATICS COURSES Grades 8-12 2015-2016 Calculus III H Calculus II H A.P. Calculus BC A.P. Statistics A.P. Calculus AB A.P. Calculus BC Algebra II H* Pre-Calculus H Calculus/Stats H A.P. Calculus AB

More information

CS & Applied Mathematics Dual Degree Curriculum Content

CS & Applied Mathematics Dual Degree Curriculum Content CS & Applied Mathematics Dual Degree Curriculum Content General Education (41 credits) COMM 101: Written and Oral Communication I COMM 301: Written and Oral Communication II ECON 201: Economic Principles

More information

Bachelor Degree in Business Administration Academic year 2015/16

Bachelor Degree in Business Administration Academic year 2015/16 University of Catania Department of Economics and Business Bachelor Degree in Business Administration Academic year 2015/16 Mathematics for Social Sciences (1st Year, 1st Semester, 9 Credits) Name of Lecturer:

More information

Algebra I Credit Recovery

Algebra I Credit Recovery Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,

More information

COWLEY COLLEGE & Area Vocational Technical School

COWLEY COLLEGE & Area Vocational Technical School COWLEY COLLEGE & Area Vocational Technical School COURSE PROCEDURE FOR DIFFERENTIAL EQUATIONS MTH 4465 3 Credit Hours Student Level: This course is open to students on the college level in the sophomore

More information

APPLIED MATHEMATICS ADVANCED LEVEL

APPLIED MATHEMATICS ADVANCED LEVEL APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

More information

DRAFT. Further mathematics. GCE AS and A level subject content

DRAFT. Further mathematics. GCE AS and A level subject content Further mathematics GCE AS and A level subject content July 2014 s Introduction Purpose Aims and objectives Subject content Structure Background knowledge Overarching themes Use of technology Detailed

More information

Mathematics Program Description Associate in Arts Degree Program Outcomes Required Courses............................. Units

Mathematics Program Description Associate in Arts Degree Program Outcomes Required Courses............................. Units Program Description Successful completion of this maj will assure competence in mathematics through differential and integral calculus, providing an adequate background f employment in many technological

More information

Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

More information

Algebra 1 Course Title

Algebra 1 Course Title Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

More information

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).

More information

X On record with the USOE.

X On record with the USOE. Textbook Alignment to the Utah Core Algebra 2 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is

More information

Big Ideas in Mathematics

Big Ideas in Mathematics Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

More information

MATHEMATICS & STATISTICS

MATHEMATICS & STATISTICS Area: Mathematics Dean: Nancy Reitz, Interim Phone: (916) 484-8215 Counseling: (916) 484-8572 Mathematics Degree The A.S. degree in mathematics provides a foundation of mathematics for students in preparation

More information

ISU Department of Mathematics. Graduate Examination Policies and Procedures

ISU Department of Mathematics. Graduate Examination Policies and Procedures ISU Department of Mathematics Graduate Examination Policies and Procedures There are four primary criteria to be used in evaluating competence on written or oral exams. 1. Knowledge Has the student demonstrated

More information

A strong background in mathematics also facilitates employment for the following:

A strong background in mathematics also facilitates employment for the following: Mathematics School of Mathematics, Computer Science and Engineering Dean: Kathleen Schrader, DNSc Academic Chair: Miriam Castroconde Faculty: Abdulmagid Aburwein, PhD, Jack Appleman, Mohammad Araiepour,

More information

Cabrillo College Catalog 2015-2016

Cabrillo College Catalog 2015-2016 MATHEMATICS Natural and Applied Sciences Division Wanda Garner, Division Dean Division Office, Room 701 Jennifer Cass, Department Chair, (831) 479-6363 Aptos Counselor: (831) 479-6274 for appointment Watsonville

More information

MATHEMATICS. Administered by the Department of Mathematical and Computing Sciences within the College of Arts and Sciences. Degree Requirements

MATHEMATICS. Administered by the Department of Mathematical and Computing Sciences within the College of Arts and Sciences. Degree Requirements MATHEMATICS Administered by the Department of Mathematical and Computing Sciences within the College of Arts and Sciences. Paul Feit, PhD Dr. Paul Feit is Professor of Mathematics and Coordinator for Mathematics.

More information

KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007

KEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007 KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 4-47) Surveys and

More information

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary

Current Standard: Mathematical Concepts and Applications Shape, Space, and Measurement- Primary Shape, Space, and Measurement- Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two- and three-dimensional shapes by demonstrating an understanding of:

More information

HIGH SCHOOL: GEOMETRY (Page 1 of 4)

HIGH SCHOOL: GEOMETRY (Page 1 of 4) HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course

More information

MATHEMATICAL METHODS OF STATISTICS

MATHEMATICAL METHODS OF STATISTICS MATHEMATICAL METHODS OF STATISTICS By HARALD CRAMER TROFESSOK IN THE UNIVERSITY OF STOCKHOLM Princeton PRINCETON UNIVERSITY PRESS 1946 TABLE OF CONTENTS. First Part. MATHEMATICAL INTRODUCTION. CHAPTERS

More information

Master of Arts in Mathematics

Master of Arts in Mathematics Master of Arts in Mathematics Administrative Unit The program is administered by the Office of Graduate Studies and Research through the Faculty of Mathematics and Mathematics Education, Department of

More information

Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303.

Prerequisites: TSI Math Complete and high school Algebra II and geometry or MATH 0303. Course Syllabus Math 1314 College Algebra Revision Date: 8-21-15 Catalog Description: In-depth study and applications of polynomial, rational, radical, exponential and logarithmic functions, and systems

More information

Florida Math for College Readiness

Florida Math for College Readiness Core Florida Math for College Readiness Florida Math for College Readiness provides a fourth-year math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness

More information

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard

Algebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express

More information

096 Professional Readiness Examination (Mathematics)

096 Professional Readiness Examination (Mathematics) 096 Professional Readiness Examination (Mathematics) Effective after October 1, 2013 MI-SG-FLD096M-02 TABLE OF CONTENTS PART 1: General Information About the MTTC Program and Test Preparation OVERVIEW

More information

GRADES 7, 8, AND 9 BIG IDEAS

GRADES 7, 8, AND 9 BIG IDEAS Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for

More information

REQUIREMENTS FOR A 3-YEAR BA/BSc IN MATHEMATICS

REQUIREMENTS FOR A 3-YEAR BA/BSc IN MATHEMATICS MATHEMATICS (MATH) Updated June 3, 2015 Note: The department/program code MATH replaces the former codes 32. Students cannot hold credit in MATH-xxxx and the former 32.xxxx having the same course number

More information

How To Learn Math At A Junior High

How To Learn Math At A Junior High MATH DEPARTMENT COURSE DESCRIPTIONS The Mathematics Department provides a challenging curriculum that strives to meet the needs of a diverse student body by: Helping the student realize that the analytical

More information

Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades. Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)

More information

.INTL: INTERNATIONAL/INTERCULTURAL STUDIES

.INTL: INTERNATIONAL/INTERCULTURAL STUDIES .INTL: INTERNATIONAL/INTERCULTURAL STUDIES INTL 2090 Introduction to International/Intercultural Studies 3-0-3 An overview of international studies as a field of inquiry and practice. An examination of

More information

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab

MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring non-course based remediation in developmental mathematics. This structure will

More information

Unit 4: 15 Progression : Definition of A.P. & G.P., To find Tn & Sn, Simple practical commercial problems.

Unit 4: 15 Progression : Definition of A.P. & G.P., To find Tn & Sn, Simple practical commercial problems. Solapur University, Solapur. Semester Pattern Syllsbus B.Com Part I Business Mathematics (w. e. f. June 2010) Semester I Periods Unit 1: 15 Determinant & Matrices : Definition of second & Third order Determinant,

More information

Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version

Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version Brochure More information from http://www.researchandmarkets.com/reports/3148843/ Elementary Differential Equations and Boundary Value Problems. 10th Edition International Student Version Description:

More information

How To Understand And Solve Algebraic Equations

How To Understand And Solve Algebraic Equations College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

More information

APPLICATION FOR PART-TIME EMPLOYMENT AS A TUTOR TUTOR IN THE DOLCIANI MATHEMATICS LEARNING CENTER

APPLICATION FOR PART-TIME EMPLOYMENT AS A TUTOR TUTOR IN THE DOLCIANI MATHEMATICS LEARNING CENTER APPLICATION FOR PART-TIME EMPLOYMENT AS A TUTOR TUTOR IN THE DOLCIANI MATHEMATICS LEARNING CENTER Dear Applicant, As you consider applying for a position in the Dolciani Mathematics Learning Center, there

More information

MATHEMATICS (MAT) Programs Offered. Master of Science. Mathematics

MATHEMATICS (MAT) Programs Offered. Master of Science. Mathematics 110 Mathematics MATHEMATICS (MAT) 313 Stevenson Hall, (309) 438-8781 Math.IllinoisState.edu Chairperson: George F. Seelinger. Office: 313 Stevenson Hall. Graduate Program Directors: Cynthia Langrall, Michael

More information

04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators

04 Mathematics CO-SG-FLD004-03. Program for Licensing Assessments for Colorado Educators 04 Mathematics CO-SG-FLD004-03 Program for Licensing Assessments for Colorado Educators Readers should be advised that this study guide, including many of the excerpts used herein, is protected by federal

More information

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions. Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

More information

Columbia University in the City of New York New York, N.Y. 10027

Columbia University in the City of New York New York, N.Y. 10027 Columbia University in the City of New York New York, N.Y. 10027 DEPARTMENT OF MATHEMATICS 508 Mathematics Building 2990 Broadway Fall Semester 2005 Professor Ioannis Karatzas W4061: MODERN ANALYSIS Description

More information

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

More information

Massage Therapy Mathematics

Massage Therapy Mathematics Massage Therapy Mathematics MT-2701Comprehensive Somatic Studies for Massage Therapists 01 Semester Credit Quizzes and mock exam are given to prepare for State Medical Board of Ohio licensure exam. Comprehensive

More information

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

More information

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers. Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

More information

Chapter 3: Mathematical Models and Numerical Methods Involving First-Order Differential Equations

Chapter 3: Mathematical Models and Numerical Methods Involving First-Order Differential Equations Massasoit Community College Instructor: Office: Email: Phone: Office Hours: Course: Differential Equations Course Number: MATH230-XX Semester: Classroom: Day and Time: Course Description: This course is

More information

Pre-Calculus Semester 1 Course Syllabus

Pre-Calculus Semester 1 Course Syllabus Pre-Calculus Semester 1 Course Syllabus The Plano ISD eschool Mission is to create a borderless classroom based on a positive student-teacher relationship that fosters independent, innovative critical

More information

Code: MATH 274 Title: ELEMENTARY DIFFERENTIAL EQUATIONS

Code: MATH 274 Title: ELEMENTARY DIFFERENTIAL EQUATIONS Code: MATH 274 Title: ELEMENTARY DIFFERENTIAL EQUATIONS Institute: STEM Department: MATHEMATICS Course Description: This is an introductory course in concepts and applications of differential equations.

More information

Math 131 College Algebra Fall 2015

Math 131 College Algebra Fall 2015 Math 131 College Algebra Fall 2015 Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: Course Description This course has a minimal review of algebraic skills followed by a study of

More information

UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS

UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS UNIVERSITY OF PUNE, PUNE 411007. BOARD OF STUDIES IN MATHEMATICS SYLLABUS F.Y.B.Sc (MATHEMATICS) PAPER 1 ALGEBRA AND GEOMETRY FIRST TERM 1) Sets (4 Lectures) 1.1 Power set of a set, Product of two sets.

More information

MATH ADVISEMENT GUIDE

MATH ADVISEMENT GUIDE MATH ADVISEMENT GUIDE Recommendations for math courses are based on your placement results, degree program and career interests. Placement score: MAT 001 or MAT 00 You must complete required mathematics

More information

About Tutorials... 1 Algebra I... 2 Geometry... 3 Algebra II... 4 English I... 5 English II... 6 English III... 7

About Tutorials... 1 Algebra I... 2 Geometry... 3 Algebra II... 4 English I... 5 English II... 6 English III... 7 Outlines Texas Tutorials Apex Learning Texas Tutorials provide teachers with a solution to support all students in rising to the expectations established by the Texas state standards. With content developed

More information

Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year. This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

More information

Math Placement Test Sample Problems PRE-ALGEBRA

Math Placement Test Sample Problems PRE-ALGEBRA Math Placement Test Sample Problems The Math Placement Test is an untimed, multiple-choice, computer-based test. The test is composed of four sections: pre-algebra, algebra, college algebra, and trigonometry.

More information

College Credit Plus Dual Enrollment

College Credit Plus Dual Enrollment Plus Dual Enrollment Plus Dual Enrollment is a program that gives high school students an opportunity to be enrolled in both high school and college course work at the same time. Students who qualify academically

More information

Math 1050 Khan Academy Extra Credit Algebra Assignment

Math 1050 Khan Academy Extra Credit Algebra Assignment Math 1050 Khan Academy Extra Credit Algebra Assignment KhanAcademy.org offers over 2,700 instructional videos, including hundreds of videos teaching algebra concepts, and corresponding problem sets. In

More information

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems

Pre-Algebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems Academic Content Standards Grade Eight Ohio Pre-Algebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small

More information

MATHEMATICS Department Chair: Michael Cordova - mccordova@dcsdk12.org

MATHEMATICS Department Chair: Michael Cordova - mccordova@dcsdk12.org MATHEMATICS Department Chair: Michael Cordova - mccordova@dcsdk12.org Course Offerings Grade 9 Algebra I Algebra II/Trig Honors Geometry Honors Geometry Grade 10 Integrated Math II (2014-2015 only) Algebra

More information

Mathematics I, II and III (9465, 9470, and 9475)

Mathematics I, II and III (9465, 9470, and 9475) Mathematics I, II and III (9465, 9470, and 9475) General Introduction There are two syllabuses, one for Mathematics I and Mathematics II, the other for Mathematics III. The syllabus for Mathematics I and

More information

Birmingham City Schools

Birmingham City Schools Activity 1 Classroom Rules & Regulations Policies & Procedures Course Curriculum / Syllabus LTF Activity: Interval Notation (Precal) 2 Pre-Assessment 3 & 4 1.2 Functions and Their Properties 5 LTF Activity:

More information

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS

AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS AN INTRODUCTION TO NUMERICAL METHODS AND ANALYSIS Revised Edition James Epperson Mathematical Reviews BICENTENNIAL 0, 1 8 0 7 z ewiley wu 2007 r71 BICENTENNIAL WILEY-INTERSCIENCE A John Wiley & Sons, Inc.,

More information

COLLEGE ALGEBRA LEARNING COMMUNITY

COLLEGE ALGEBRA LEARNING COMMUNITY COLLEGE ALGEBRA LEARNING COMMUNITY Tulsa Community College, West Campus Presenter Lori Mayberry, B.S., M.S. Associate Professor of Mathematics and Physics lmayberr@tulsacc.edu NACEP National Conference

More information

Questions. Strategies August/September Number Theory. What is meant by a number being evenly divisible by another number?

Questions. Strategies August/September Number Theory. What is meant by a number being evenly divisible by another number? Content Skills Essential August/September Number Theory Identify factors List multiples of whole numbers Classify prime and composite numbers Analyze the rules of divisibility What is meant by a number

More information

College of Arts and Sciences. Mathematics

College of Arts and Sciences. Mathematics 108R INTERMEDIATE ALGEBRA. (3) This course is remedial in nature and covers material commonly found in second year high school algebra. Specific topics to be discussed include numbers, fractions, algebraic

More information

What are the place values to the left of the decimal point and their associated powers of ten?

What are the place values to the left of the decimal point and their associated powers of ten? The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

More information

Pre-Engineering INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu

Pre-Engineering INDIVIDUAL PROGRAM INFORMATION 2014 2015. 866.Macomb1 (866.622.6621) www.macomb.edu Pre-Engineering INDIVIDUAL PROGRAM INFORMATION 2014 2015 866.Macomb1 (866.622.6621) www.macomb.edu Pre Engineering PROGRAM OPTIONS CREDENTIAL TITLE CREDIT HOURS REQUIRED NOTES Associate of Science Pre

More information