DOCSLIB.ORG

MATHEMATICS (MATH) College of Alameda 2019-2020 Catalog MATHEMATICS (MATH) MATHEMATICS

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
MATHEMATICS (MATH) College of Alameda 2019-2020 Catalog MATHEMATICS (MATH) MATHEMATICS 212 • MATHEMATICS (MATH) College of Alameda 2019-2020 Catalog MATHEMATICS (MATH) MATHEMATICS What is Mathematics? Studying math is an exploration MATH 3A of the “science of numbers and their operations, Calculus I interrelations, combinations, generalizations, and 5 units, 5 hours lecture (GR) abstractions and of space configurations and their Prerequisite: Math 2, or Math 1 and 50 structure, measurement, transformations, and Acceptable for credit: CSU, UC generalizations.” (Merriam-Webster) Theorems on limits and continuous functions, derivatives, differentials and applications: Fundamental At College of Alameda we offer you a variety of courses theorems of calculus and applications; properties of intended for those who want to pursue a degree or exponential, logarithmic, and inverse trigonometric certificate in mathematics as well as those who wish to functions, and hyperbolic functions. 1701.00 develop quantitative and problem-solving skills for use AA/AS area 4b; CSU area B4; IGETC area 2 in other fields. We teach according to the motto: C-ID MATH 210 Education anytime anywhere by offering a wide MATH 3B range of Math classes designed to fit around anyone’s Calculus II busy schedules. 5 units, 5 hours lecture (GR) Prerequisite: Math 3A The faculty and staff in mathematics at College of Acceptable for credit: CSU, UC Alameda are dedicated to working hard with you— Applications of the definite integral: Methods of helping you succeed in a positive atmosphere that is integration, polar coordinates, parametric equations, conducive to your learning math in the most enjoyable infinite and power series. 1701.00 and competent manner possible. AA/AS area 4b; CSU area B4; IGETC area 2 MATH 1 MATH 3C Pre-Calculus Calculus III 4 units, 4 hours lecture 5 units, 5 hours lecture (GR) Prerequisite: Math 203 or Math 211D or Math 230 Prerequisite: Math 3B Acceptable for Credit: CSU, UC Acceptable for credit: CSU, UC Preparation for the calculus sequence or other courses Partial differentiation: Jacobians, transformations, requiring a sound algebraic background: Inequalities, multiple integrals, theorems of Green and Stokes, theory of equations, sequences and series, matrices, differential forms, vectors and vector functions, functions and relations, logarithmic and exponential geometric coordinates, and vector calculus. 1701.00 functions; function concept used as a unifying notion. AA/AS area 4b; CSU area B4; IGETC area 2 1701.00 C-ID MATH 230 AA/AS area 4B MATH 3E MATH 2 Linear Algebra Pre-Calculus with Analytic Geometry 3 units, 3 hours lecture (GR) 5 units, 5 hours lecture (GR) Prerequisite: Math 3A Prerequisite: Math 50 Not open for credit to students who have completed or Acceptable for credit: CSU, UC are currently enrolled in Math 3D. Advanced algebra and analytic geometry: Linear, Acceptable for credit: CSU, UC quadratic, polynomial, rational, exponential, logarithmic, Linear algebra: Gaussian and Gauss-Jordan elimination, and inverse functions; determinants, matrices and linear matrices, determinants, vectors in R2 and R3, real and systems; zeros to polynomials, arithmetic and geometric complex vector spaces, inner product spaces, linear sequences, mathematical induction; permutations and transformations, eigenvalues, eigenvectors, and combinations, binomial theorem; vectors, conic sections, applications. 1701.00 translation and rotation of axes, polar coordinates, lines AA/AS area 4b; CSU area B4; IGETC area 2 and surfaces in space, quadric surfaces. 1701.00 C-ID MATH 250 AA/AS area 4b; CSU area B4; IGETC area 2 College of Alameda 2019-2020 Catalog MATHEMATICS (MATH) • 213 MATH 3F MATH 15 Differential Equations Mathematics for Liberal Arts Students 3 units, 3 hours lecture (GR) 3 units, 3 hours lecture (GR or P/NP) MATHEMATICS Prerequisite: Math 3B and 3E Prerequisites: MATH 203 or 211D or 230 or 240 or Recommended Preparation: Math 3C equivalent Math 3E plus 3F are equivalent to Math 3D. Eligible for credit by examination Not open for credit to students who have completed or Acceptable for credit: CSU, UC are currently enrolled in Math 3D. Fundamental ideas underlying modern mathematics: Acceptable for credit: CSU, UC Elements from logic, sets, and number systems; concepts Ordinary differential equations: First-order, second- of elementary algebra, geometry, topology, and order, and higher-order equations; separable and exact combinatorics. 1701.00 equations, series solutions, Laplace transformations, AA/AS area 4b; CSU area B4 systems of differential equations. 1701.00 AA/AS area 4b; CSU area B4; IGETC area 2 MATH 16A C-ID MATH 240 Calculus for Business and Life/Social Sciences 3 units, 3 hours lecture (GR) MATH 11 Prerequisite: Math 2 Discrete Mathematics Eligible for credit by examination 4 units, 4 hours lecture (GR or P/NP) Acceptable for credit: CSU, UC Prerequisite: Math 3B Introduction to analytic geometry and differential and Acceptable for credit: CSU, UC integral calculus of algebraic functions with particular Discrete mathematics: Mathematical induction, finite attention paid to simple applications. 1701.00 series, sets, relations and functions, introduction to trees, AA/AS area 4b; CSU area B4; IGETC area 2 combinatorics, algebraic structures, and probability. 1701.00 MATH 48AA-FZ AA/AS area 4b; CSU area B4; IGETC area 2 Selected Topics in Mathematics .5-5 units, 0-5 hours lecture, 0-15 hours laboratory MATH 13 (GR or P/NP) Introduction to Statistics Acceptable for credit: CSU 4 units, 4 hours lecture (GR) See section on Selected Topics. 1701.00 Prerequisite: Math 203 or Math 206 or Math 211D or Math 230 or Math 240 or appropriate placement through MATH 49 multiple-measures assessment process Independent Study in Mathematics Acceptable for credit: CSU, UC .5-5 units, .5-5 hours lecture (GR) Introduction to theory and practice of statistics: Collecting Acceptable for credit: CSU data: Sampling, observational and experimental studies. See section on Independent Study. 1701.00 Organizing data: Univariate and bivariate tables and graphs, histograms. Describing data: Measures of MATH 50 location, spread, and correlation. Theory: Probability, Trigonometry random variables; binomial and normal distributions. 3 units, 3 hours lecture (GR) Drawing conclusions from data: Confidence intervals, Prerequisite: Math 203 or Math 211D or Math 230 hypothesis testing, z-tests, t-tests, and chi-square tests; Recommended Preparation: Math 202 one-way analysis of variance. Regression and non- Not open for credit to students who have completed or parametric methods. 1701.00 are currently enrolled in Math 52ABC. AA/AS area 4b; CSU area B4; IGETC area 2 Eligible for credit by examination C-ID MATH 110 Acceptable for credit: CSU Introduction to functional trigonometry: Basic definitions, identities, graphs, inverse functions, trigonometric equations and applications, solution of triangles and applications, polar coordinates, complex numbers, and De Moivre’s Theorem. 1701.00 AA/AS area 4b; CSU area B4 214 • MATHEMATICS (MATH) College of Alameda 2019-2020 Catalog MATH 201 MATH 206 Elementary Algebra Algebra for Statistics MATHEMATICS 4 units, 5 hours lecture (GR) 5 units, 6 hours lecture (GR) Prerequisite: Math 225, 250 or 253 or appropriate Prerequisite: Math 253 or appropriate placement through placement through multiple measures assessment multiple measures assessment process process Integrated mathematics for statistics: Exploratory Not open for credit to students who have completed or data analysis and principles of data collection and are currently enrolled in Math 210ABCD. calculation; ratios, rates, and proportional reasoning; Eligible for credit by examination fractions, decimals and percents; evaluating expressions; Basic algebraic operations: Linear equations and analyzing algebraic expressions of statistical measures; inequalities, relations and functions, factoring quadratic modeling bivariate data with linear and exponential polynomials, solving quadratic equations, fractions, functions; graphical and numerical descriptive statistics radicals and exponents, word problems, graphing, and for quantitative and categorical data. Not recommended number systems. 1701.00 for science, technology, engineering, mathematics, nursing or business majors. 1701.00 MATH 202 Geometry MATH 213 3 units, 3 hours lecture (GR) Support for Statistics Prerequisite: Math 201 or Math 210D or appropriate 2 units, 2 hours lecture (P/NP) placement through multiple-measures assessment Corequisite: Math 13 process Competencies and concepts needed in statistics: Eligible for credit by examination arithmetic, pre-algebra, elementary and intermediate Introduction to plane geometry emphasizing algebra, and descriptive statistics; descriptive data mathematical logic and proofs: Geometric constructions, analysis, solving and graphing linear equations, and congruent triangles, parallel lines and parallelograms, modeling with linear functions. Intended for students proportions, similar triangles, circles, polygons, and who are concurrently enrolled in MATH 13. 1701.00 area. 1701.00 AA/AS area 4b MATH 215 Support for Pre-Calculus MATH 203 2 Units, 2 hours lecture (P/NP) Intermediate Algebra Corequisites: Math 1 4 units, 5 hours lecture (GR) Recommended Preparation: This course is appropriate Prerequisite: Math 201 or Math 210D or appropriate for students who are confident in their graphing and placement through multiple-measures assessment beginning algebra skills. process Review of the core prerequisite skills, competencies, and Recommended preparation: Math 202
Load more

Recommended publications
  • Mathematics (MATH) 1
    Mathematics (MATH) 1 MATH 021 Precalculus Algebra 4 Units MATHEMATICS (MATH) Students will study topics which include basic algebraic concepts, complex numbers, equations and inequalities, graphs of functions, linear MATH 013 Intermediate Algebra 5 Units and quadratic functions, polynomial functions of higher degree, rational, This course continues the Algebra sequence and is a prerequisite to exponential, absolute value, and logarithmic functions, sequences and transfer level math courses. Students will review elementary algebra series, and conic sections. This course is designed to prepare students topics and further their skills in solving absolute value in equations for the level of algebra required in calculus. Students may not take a and inequalities, quadratic functions and complex numbers, radicals combination of MATH 021 and MATH 025. (C-ID MATH 151) and rational exponents, exponential and logarithmic functions, inverse Lecture Hours: 4 Lab Hours: None Repeatable: No Grading: L functions, and sequences and series. Prerequisite: MATH 013 with C or better Lecture Hours: 5 Lab Hours: None Repeatable: No Grading: O Advisory Level: Read: 3 Write: 3 Math: None Prerequisite: MATH 111 with P grade or equivalent Transfer Status: CSU/UC Degree Applicable: AA/AS Advisory Level: Read: 3 Write: 3 Math: None CSU GE: B4 IGETC: 2A District GE: B4 Transfer Status: None Degree Applicable: AS Credit by Exam: Yes CSU GE: None IGETC: None District GE: None MATH 021X Just-In-Time Support for Precalculus Algebra 2 Units MATH 014 Geometry 3 Units Students will receive "just-in-time" review of the core prerequisite Students will study logical proofs, simple constructions, and numerical skills, competencies, and concepts needed in Precalculus.
    [Show full text]
  • ACT Info for Parent Night Handouts
    The following pages contain tips, information, how to buy test back, etc. From ACT.org Carefully read the instructions on the cover of the test booklet. Read the directions for each test carefully. Read each question carefully. Pace yourself—don't spend too much time on a single passage or question. Pay attention to the announcement of five minutes remaining on each test. Use a soft lead No. 2 pencil with a good eraser. Do not use a mechanical pencil or ink pen; if you do, your answer document cannot be scored accurately. Answer the easy questions first, then go back and answer the more difficult ones if you have time remaining on that test. On difficult questions, eliminate as many incorrect answers as you can, then make an educated guess among those remaining. Answer every question. Your scores on the multiple-choice tests are based on the number of questions you answer correctly. There is no penalty for guessing. If you complete a test before time is called, recheck your work on that test. Mark your answers properly. Erase any mark completely and cleanly without smudging. Do not mark or alter any ovals on a test or continue writing the essay after time has been called. If you do, you will be dismissed and your answer document will not be scored. If you are taking the ACT Plus Writing, see these Writing Test tips. Four Parts: English (45 minutes) Math (60 minutes) Reading (35 minutes) Science Reasoning (35 minutes) Content Covered by the ACT Mathematics Test In the Mathematics Test, three subscores are based on six content areas: pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry.
    [Show full text]
  • And Intermediate Algebra (MAT 099) Course Articulation Agreement
    MCHENRY COUNTY COLLEGE AND MCHENRY COUNTY COOPERATIVE FOR EMPLOYMENT EDUCATION COURSE ARTICULATION AGREEMENT FOR Elementary Algebra (MAT 095) Intermediate Algebra (MAT 099) 1. Beginning with graduating class of 2017, the following policies are in effect: A. Completion of articulation classes with a grade of (A), (B), or (C), and (C- or better) in both semesters of geometry, then • Eligible to enroll in MAT 161, MAT 165, MAT 201 and exempt from the ALEKS math placement test B. Completion of articulation classes with a grade of (A), (B), or (C), but did not meet the geometry requirement, then • Eligible to enroll in MAT 120 and/or MAT 150 and exempt from the ALEKS math placement test. DISTRICT DISTRICT COURSE TITLE Alden-Hebron #19 Introduction to College Algebra Cary Grove #155 391 College Algebra Crystal Lake Central #155 391 College Algebra Crystal Lake South #155 391 College Algebra Harvard #50 MAT 095/MAT 099 McHenry East #156 Transitions to College Math McHenry West #156 Transitions to College Math Prairie Ridge #155 391 College Algebra Woodstock HS #200 Introduction to College Algebra Woodstock North #200 Introduction to College Algebra Approved Programs: MAT 095 and MAT 099 – Credit cannot be applied to a degree or certificate. 2. Successful completion of MAT 095 and MAT 099 in high school meets the same requirements as if taken at MCC. 3. The student must be enrolled at MCC on the 10th day of the semester, within 27 months following high school graduation. 4. The college course covered by this articulated agreement is designed to lead to enrollment in one of the following credit bearing mathematics classes: A.
    [Show full text]
  • Elementary Algebra > Syllabus
    San Antonio College · - · MATH-Mathematics Elementary Algebra MATH-0410 Summer - 8 Week Session Summer 2018 Section 026.14294 4-4-1 Credits 06/04/2018 to 07/26/2018 Modified 05/31/2018 Contact Information Professor Roland Treviño McCreless Hall, MCCH 126C [email protected] (Canvas email preferred) Math Department – MCCH 221 – 210.486.0270 Administrative Services Specialist - Patricia Gonzalez – [email protected] Academic Unit Assistant - Cynthia Morton – [email protected] Program Coordinator - Paula McKenna – [email protected] Department Chair – Dr. Said Fariabi – [email protected] Materials PREREQUISITES, CO-REQUISITES and OTHER REQUIREMENTS: Prerequisite(s):TSI score MATH Numeracy 310-335 with ABE 3 -6. Course placement advisement is available in the Mathematics/Computer Science Office located at MCCH 221. TEXTBOOKS (including ISBN#) and REQUIRED MATERIALS/RECOMMENDED READINGS: The student should go to www.connectmath.com to register for the online math program that accompanies this course. Register as a new student even if you have used this program in the past. You will be asked for the following Course Code: E4AFH-YHTVQ You already purchased access to this program at registration. There is no need for any more purchases beyond this. COURSE CONTENT: Topics include those listed below. Please see the Methods of Measurement section below to see other requirements such as exams. Chapter 1: Whole Numbers 1.2 – 1.6 (REVIEW ONLY) 1.7 Exponents, Algebraic Expressions, and the Order of Operations Chapter 2: Integers and Algebraic
    [Show full text]
  • Elementary Algebra
    ELEMENTARY ALGEBRA 10 Overview The Elementary Algebra section of ACCUPLACER contains 12 multiple choice Algebra questions that are similar to material seen in a Pre-Algebra or Algebra I pre-college course. A calculator is provided by the computer on questions where its use would be beneficial. On other questions, solving the problem using scratch paper may be necessary. Expect to see the following concepts covered on this portion of the test: Operations with integers and rational numbers, computation with integers and negative rationals, absolute values, and ordering. Operations with algebraic expressions that must be solved using simple formulas and expressions, adding and subtracting monomials and polynomials, multiplying and dividing monomials and polynomials, positive rational roots and exponents, simplifying algebraic fractions, and factoring. Operations that require solving equations, inequalities, and word problems, solving linear equations and inequalities, using factoring to solve quadratic equations, solving word problems and written phrases using algebraic concepts, and geometric reasoning and graphing. Testing Tips Use resources provided such as scratch paper or the calculator to solve the problem. DO NOT attempt to only solve problems in your head. Start the solving process by writing down the formula or mathematic rule associated with solving the particular problem. Put your answer back into the original problem to confirm that your answer is correct. Make an educated guess if you are unsure of the answer. 11 Algebra
    [Show full text]
  • MATH 101-Elementary Algebra Reedley College, Fall 2011 Daily 10:00-10:50Pm, FEM-4E Schedule Number: 56423 August 15
    MATH 101-Elementary Algebra Reedley College, Fall 2011 Daily 10:00-10:50pm, FEM-4E Schedule Number: 56423 August 15 - December 16 Instructor: Becky Reimer [email protected] Office Hours: As a part-time instructor, I do not have an office on campus. If you need to contact me, use the email address provided above. This semester I will be available on Mondays and Wednesdays in the Math Center from 11:00-12:00. Important Dates: Sept 5 Labor Day – no classes Oct 14 Last Day to drop this class (Grades given after this date) Nov 10 Veterans Day – no classes Nov 24-25 Thanksgiving Holiday – no classes Dec 14 Final Exam Textbook: George Woodbury, Elementary and Intermediate Algebra, Third Edition Required Materials: Graph Paper Sharpened pencils (preferably mechanical with extra lead) Erasers 3-ring binder to hold notes and assignments Textbook: online version required, hardcopy optional Blackboard: A blackboard website will be maintained for this course. http://blackboard.reedleycollege.edu Your user name and password for this website are your student I.D. number. This syllabus, as well as all homework assignments and announcements, can be found on this website. Attendance: You are expected to attend all class sessions, arrive on time, and stay for the entire session. If you are absent ten (10) or more times by October 14, you will be dropped from the course. Behavior: You will be expected to treat yourselves and others with respect and kindness. Please turn off cell phones and any other electronic devices before class begins. Academic Honesty: Academic integrity is essential to a successful college career.
    [Show full text]
  • Mathematics Courses
    COURSES COURSES MATHEMATICS COURSES MAT 003A Analytic Geometry and Calculus I (5.0 Lecture) 5.0 UNITS MAT 000B Plane Geometry 4.0 UNITS Prerequisite: MAT 002 or placement into the course by the Mission College Prerequisite: MATH 903 or satisfactory score on an appropriate Mathematics Mathematics Placement Exam. ; or Prerequisite: MAT 000D or higher or Placement Exam. Basic concepts of plane geometry for lines, planes, triangles satisfactory score on an appropriate Mathematics Placement Exam. and and spheres and an introduction to deductive reasoning. Pass/No Pass Prerequisite: MAT 001 or placement into the course by the Mission College Option. Mathematics Placement Exam. This is the first part of the three-semester calculus sequence. Topics include functions,limits, continuity, differentiation and integration, and applications for polynomial and transcendental MAT 000C Intermediate Algebra (5.0 Lecture) 5.0 UNITS functions. C-ID # MATH 210. Prerequisite: Completion of the Mission College Placement Assistance Tool prior to registration. The student will study fundamental laws of exponents and radicals, quadratic equations, graphical representations, complex MAT 003AH Analytic Geometry and Calculus I - Honors (5.0 numbers, functions and inverses, logarithmic and exponential functions, Lecture) 5.0 UNITS conic sections, sequences and series, linear systems and inequalities, and Prerequisite: MAT 002 or placement into the course by the Mission College applied problems. Mathematics Placement Exam. ; or Prerequisite: MAT 000D or placement into the course by the Mission College Mathematics Placement Exam. and Prerequisite: MAT 001 or placement into the course by the Mission College MAT 000CM Intermediate Algebra (MAPS) (5.0 Mathematics Placement Exam. This course is the honors version of the Lecture) 5.0 UNITS Calculus I course and is the first part of the three-semester calculus sequence Prerequisite: Completion of the Mission College Placement Assistance Tool for math, physics and engineering majors.
    [Show full text]
  • Elementary Algebra for Adults That Do Not Know Algebra
    Ç××ifÖage aÒd AÐgebÖa David A. SANTOS [email protected] July 17, 2008 Version If there should be another flood Hither for refuge fly Were the whole world to be submerged This book would still be dry.1 1Anonymous annotation on the fly leaf of an Algebra book. Free to photocopy and distribute ii Copyright © 2007 David Anthony SANTOS. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”. GNU Free Documentation License Version 1.2, November 2002 Copyright © 2000,2001,2002 Free Software Foundation, Inc. 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The purpose of this License is to make a manual, textbook, or other functional and useful document “free” in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others. This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense.
    [Show full text]
  • MATH 0302 — Elementary Algebra and Geometry Frank Phillips College
    MATH 0302 — Elementary Algebra and Geometry Frank Phillips College General Course Information Credit Hours: 3 Prerequisite Placement by an approved TSI test. (Does not count toward a degree.) Course Description Algebraic expressions, linear equations and models, exponents, and polynomials, factoring, algebraic fractions, graphing, systems of linear equations, radicals, points, parallel and perpendicular lines, planes, space angles, triangles, congruent triangles, space figures, volume, surface, area, reasoning skills. THECB Approval Number ............................................................................32.0104.51.19 Learning Outcomes Upon successful completion of this course, students will be able to: 1. Develop the basic tools of algebra needed for further courses in mathematics; 2. Show that mathematics is useful in many disciplines using applications; 3. Evaluate algebraic expressions; 4. Convert phrases to algebraic expressions; 5. Graph and order real numbers on the number line; 6. Find absolute values and opposites of real numbers; 7. Add, subtract, multiply, and divide real numbers; 8. Use and identify properties of real numbers; 9. Combine algebraic expressions; 10. Solve linear equations; 11. Solve linear inequalities; 12. Use integer exponents; 13. Do arithmetic operations on polynomials; 14. Factor polynomials; 15. Simplify rational expressions; 16. Use the rectangular coordinate system to do simple graphing; 17. Evaluate and estimate square roots and other basic radicals; 18. Identify and calculate the measures of adjacent, vertical, and complementary angles; 19. Investigate properties of parallel and perpendicular lines; 20. Work with congruent and similar triangles; and 21. Solve systems of equations in two variables. Methods of Evaluation Category Percentage Homework, class work, labs, and quizzes 25% Major Exams 50% Final Exam 25% Total 100% Academic Honesty and Integrity Students attending Frank Phillips College are expected to maintain high standards of personal and scholarly conduct.
    [Show full text]
  • Elementary Algebra Practice Problems
    Math Placement Test Practice: Elementary Algebra Operations with Integers (Evaluate each expression.) 1. | 7| | | 2. −7 3. | 7| 4. −2 −+ 1 5 6 5. ( 3) 6( 2) 4 ( 8) ( ) 6. 32− −÷ 5− 3− (−2) − − 2 7. 3 12 ÷−3 2 +∙ −2 15 ÷ 3 − ∙ ∙ Operations with Fractions (Evaluate each expression.) ( ) 8. 4 6−1 2 3 −9 9. 3 2 −8 2 2 10. 2 +−3 + 4 3 2 5 10 3 11. ÷ 2 2 5 1 5 3 3 12. + ∙ ÷ ∙ 3 1 2 8 1 23 + 6�5 5� 7− �2 ∙ � 13. 2 14. (2 5∙ �)4÷−4 � 2 15. − + 3 1 3 2 2 5 16. � − 2� ÷ + 1 4 3 �3 − � �− 9 2� Percentages, Decimals, and Fractions 17. Order from least to greatest: , , , , , 1 1 3 3 4 8 3 4 4 5 6 10 18. Write as a decimal. 3 19. Write 8120% as a simplified fraction. 20. 4 is 25% of what number? 21. 15 is what percent of 40? 22. What is 84% of 600? Geometric Computations 23. Find the area and perimeter of a rectangle that is 6 by 9 . 24. Find the exact area and circumference of a circle with a diameter of 8 . Also compute the approximate values to the nearest thousandth. 25. Find the area of the triangle shown 5 cm 5 cm 4 cm 6 cm Operations with Algebraic Expressions Simplify each expression 26. (4 + 6 + 9 8) (6 9 7 + 3) ( 3 ) 2 ( ) 4 2 27. 5 + 3 +− +−8(6 −) − (2 ) 2 28. 6 13 +− − ( ) 29. 4− 11 6 + 25 30.
    [Show full text]
  • Vectors and Matrices (Theorems with Proof)
    Part IA | Vectors and Matrices Theorems with proof Based on lectures by N. Peake Notes taken by Dexter Chua Michaelmas 2014 These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine. Complex numbers Review of complex numbers, including complex conjugate, inverse, modulus, argument and Argand diagram. Informal treatment of complex logarithm, n-th roots and complex powers. de Moivre's theorem. [2] Vectors 3 Review of elementary algebra of vectors in R , including scalar product. Brief discussion n n of vectors in R and C ; scalar product and the Cauchy-Schwarz inequality. Concepts of linear span, linear independence, subspaces, basis and dimension. Suffix notation: including summation convention, δij and "ijk. Vector product and triple product: definition and geometrical interpretation. Solution of linear vector equations. Applications of vectors to geometry, including equations of lines, planes and spheres. [5] Matrices Elementary algebra of 3 × 3 matrices, including determinants. Extension to n × n complex matrices. Trace, determinant, non-singular matrices and inverses. Matrices as linear transformations; examples of geometrical actions including rotations, reflections, dilations, shears; kernel and image. [4] Simultaneous linear equations: matrix formulation; existence and uniqueness of solu- tions, geometric interpretation; Gaussian elimination. [3] Symmetric, anti-symmetric, orthogonal, hermitian and unitary matrices. Decomposition of a general matrix into isotropic, symmetric trace-free and antisymmetric parts. [1] Eigenvalues and Eigenvectors Eigenvalues and eigenvectors; geometric significance. [2] Proof that eigenvalues of hermitian matrix are real, and that distinct eigenvalues give an orthogonal basis of eigenvectors.
    [Show full text]
  • Motivating Abstract with Elementary Algebra
    Motivating Abstract with Elementary Algebra Timothy W. Jones October 17, 2019 Abstract There are natural lead ins to abstract algebra that occur in elementary algebra. We explore function composition and permutations as such lead ins to group theory and abstract algebra. Introduction You like math and are a math major. You’ve picked up a book on abstract algebra and are feeling a little bit queasy by what you see. Relax. This is a tutorial for you to make the transition from algebra 2, pre-calc, and the like to abstract less anxiety provoking. We’ll motivate groups in particular. Linear functions Groups look at the properties that composition of functions have. You have noticed that functions can have inverses, for example, and that sometimes f ı g ¤ g ı f . Consider linear functions, y D f.x/ D mx C b with m ¤ 0. We will make this a set with LF Œx and prove that LFŒx is closed, meaning the composition of two elements is itself in the set. Theorem 1. LFŒx is closed under function composition. Proof. Suppose f1.x/ D m1x C b1 and f2.x/ D m2x C b2 and m1 and m2 are not zero, i.e. f1; f2 2 LFŒx. Then f1.f2.x// D m1.m2x C b2/ C b1 D m1m2x C m1b2 C b1 2 LFŒx 1 Easy enough. We might mention that the slopes m are any non-zero re- als. We could limit m to non-zero rationals or natural numbers and maintain this closure property. This is a common theme of abstract algebra.
    [Show full text]