Mathematics and Computer Science Department. Grambling State University Course Syllabus. MATH 147 Pre-calculus I

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1 Mathematics and Computer Science Department College of Arts and Sciences Grambling State University Course Syllabus MATH 147 Pre-calculus I Required Text: Narasimhan, Revathi, Precalculus : Building Concepts and Connections, Houghton Mifflin, Materials: Textbook and a Hard Bound Notebook Prerequisite: A score of 17 or above on ACT (Math) or a score of 420 or above on SAT, or a grade of C or above in MATH 099 I. Course Description: Studies of Elementary logic; Set operation; Properties of real and complex numbers; Algebraic expressions; Equations and inequalities; Functions and graphs; Polynomials and rational functions; theory of polynomials, Inverse functions; Exponential functions; Logarithmic functions; Hyperbolic functions; Systems of linear equations and inequalities; Matrices and determinants, Sequences; Series; Mathematical induction; Coordinates and curves; and a Special Project. II. Rationale Pre-calculus I is the first course in a sequence of two pre-calculus courses (MATH 147 and MATH148) offered to GSU students in their General Education Curriculum. The course is designed to provide knowledge of algebra contents to enhance mathematics background and provide them tools to use in their major. This course provides opportunity for students to prepare for the mathematics portion of the MAPP (Measure of Academic Proficiency and Progress) Test which serves as a Rising Junior Examination at GSU. This course also provides the students with the necessary foundation to pursue calculus. Therefore, many learning outcomes are included in the course. Emphasis is on general mathematical concepts that are needed to enhance analytical thinking and quantitative reasoning to solve problems in a variety of fields. Exploration of the media supplements will help students to view Pre-calculus as a valuable tool for understanding the world outside the classroom. It represents a useful integration of learning techniques. In summary, competencies gained in MATH 147 are essential to the skills and practice needed in problem solving, a requirement for a successful individual. III. Competencies Upon successful completion of this course, students should be able to: 1. State properties of the natural, integer, rational, irrational, and real numbers and label them on real number line (SLO 1a). 2. Define complex numbers and learn their properties (SLO 1a). 3. State properties of exponents and radicals (SLO 1a). 4. Define polynomial, rational, and algebraic expressions in a general form (SLO 1a). 5. Define functions and their domain, range, odd/even functions, intercepts, symmetries, and intervals of increase and decrease (SLO 1a). 6. Define eight parent functions and draw their graphs (SLO 1a). 7. Write equations of straight lines, circles, and parabolas (SLO 1a) 8. Define the exponential and logarithmic functions and learn their properties (SLO 1a). 9. Define theoretical and empirical probabilities (SLO 1a). 10. Demonstrate an understanding of the counting numbers, for example, prime, composite, prime factorization, even, odd, factors, multiples, and divisors (SLO 1b). 11. Compare and contrast properties (closure, commutative, associative, identity, distributive, inverses) of numbers under various operations (SLO 1b). 12. Solve word problems using scientific notation (SLO 1b). 1

2 13. Draw the graphs of more complicated functions from the parent functions (SLO 1b). 14. Draw conclusions from the solutions of equations and inequalities (SLO 1b). 15. Understand the asymptotes and how to determine them (SLO 1b). 16. Add, subtract, multiply, and divide polynomials, rational, and algebraic expressions (SLO 1c). 17. Perform standard algebraic operations involving exponents and radicals (SLO 1c). 18. Factorize binomials, trinomials, rational, and algebraic expressions (SLO 1c). 19. Perform algebraic operations on complex numbers (SLO 1c). 20. Perform algebra on functions including composition and decomposition of functions (SLO 1c). 21. Find the inverse of a function (SLO 1c). 22. Solve quadratic equations and inequalities including absolute values (SLO 1c) 23. Solve equations involving exponential and logarithmic functions (SLO 1c). 24. Solve systems of simultaneous equations (SLO 1c). 25. Interpret a trend represented in a graph, or choose a graph that reflects a trend (SLO 2a) 26. Interpret the meaning of slope and intercepts of a straight line (SLO 2a). 27. Interpret the graphs of exponential and logarithmic functions (SLO 2a). 28. Solve word problems involving ratio, proportion, percent, arithmetic mean, geometric mean, and weighted average (SLO 2b). 29. Solve problems using statistical concepts such as mean, median, mode, range, standard deviation, and variation (SLO 2b). 30. Use system of simultaneous equations to solve word problems (SLO 2b). 31. Solve problems using relationships of parts of geometric figures (medians of triangles, inscribed angles in circles) and among geometric figures (congruence, similarity) (SLO 2b). 32. Solve application problems utilizing equations of straight line, circle, and parabola (SLO 2c). 33. Solve real world problems using the knowledge of functions (SLO 2c). 34. Use exponential and logarithmic equations to solve problems in a variety of situations (SLO 2c). IV. Behavioral Objectives Upon successful completion of this course, students should be able to: 1. Give examples of some properties of the real number system (SLO 1b). 2. Demonstrate the order of precedence of operations on arithmetic/algebraic expressions (SLO 1b) 3. Interpret the behavior of a system of linear systems of equations: parallel, perpendicular, and intersecting lines (SLO 1b). 4. Relate the algebra of functions to numbers (SLO 1b) 5. Discuss the meaning and significance of an inverse function (SLO 1b). 6. Use shifting, reflecting, and stretching techniques to graphs of functions (SLO 1b). 7. Draw the graphs of some basic quadratic functions and explain their behavior (SLO 1b). 8. Express the significance of asymptotes and analyze horizontal and vertical asymptotes (SLO 1b). 9. Develop nth term or a recursive formula for a sequence/series from a set of given numbers (SLO 1b) 10. Determine the inverse of a function (SLO 1c). 11. Compare different visual description of data: tabular, graphical, analytical, and verbal (SLO 2a). 12. Interpret behavior of a process mathematically using graphs, tables, or algebraic expressions (SLO 2a). 13. Solve problems utilizing the principles of probability (SLO 2b). 14. Solve problems using Pythagorean Theorem and its converse (SLO 2b). 15. Identify independent and dependent variables and solve real world problems from different areas (SLO 2c). 16. Model a variety of processes using polynomial, exponential, and logarithmic functions (SLO 2c). 17. Use the fundamental theorem of algebra to determine the zeros of a polynomial function. 18. Recognize fallacies and analyze arguments. 19. Perform basic set operations. 20. Understand Sequences and series. 21. Understand the Binomial Theorem. 22. Understand Proofs by Mathematical Induction. 23. Find the sums of arithmetic and geometric sequences, as well as apply series to problems. V. Course Content A. Review of Arithmetic and Geometry; Review of MAPP Test (mathematics part) B. Critical Thinking 1. Number Systems and their evolution 2

3 2. Recognizing Fallacies 3. Set and Venn Diagrams 4. Analyzing Arguments 5. Critical Thinking in Everyday Life C. Special Project A special project will be given to research the work of prominent mathematicians (assigned by the Instructor). D. Functions and their Graphs 1. Rectangular Coordinates 2. Graphs of Equations 3. Linear Equations in two variables 4. Functions 5. Analyzing Graphs of Functions 6. A library of Parent Functions 7. Transformations of Functions 8. Combinations of Functions: Composite Functions 9. Inverse Functions 10. Mathematical Modeling E. Polynomial and Rational Functions 1. Quadratic Functions and Models 2. Polynomial Functions of Higher Degree 3. Polynomial and Synthetic Division 4. Complex Numbers 5. Zeros of Polynomial Functions 6. Rational Functions F. Exponential and Logarithmic Functions 1. Exponential Functions and their Graphs 2. Logarithmic Functions and their Graphs 3. Properties of Logarithms 4. Solving Logarithmic and Exponential Equations 5. Exponential and Logarithmic Models F. Sequences and Series 1. Summation Notation 2. Sequences and Series 3. Arithmetic Sequences and Series 4. Geometric Sequences and Series V. Learning Activities Learning activities include lectures, problem-solving sessions; scientific and graphing calculator usage VI General Requirements (Turn off cell phones!) All relevant GSU policies and regulations shall apply. Per Student Handbook, violation of student code can lead to disciplinary action (expulsion). These include but not limited to, dishonesty, profanity, obscenity, verbal assault, aiding, and in-sighting. An I grade will only be given when extremely adverse and well-documented circumstances arise at the end of semester. It does not include making up for weak performance during the semester. In particular, the grade that the student had made until getting an I will still be included into computing the final grade after the student has completed the work necessary to alter the I grade. Cheating will not be tolerated in any form. As a minimum, students will be given a grade of zero for any quiz or examination in which cheating, fraud, or mis-representation is found. There may be extra credit work assigned in a form of individual research project presentation. Class participation includes but not limited to coming to class on time, being awake in the class, and not distracting other students from listening to the class lecture, and asking relevant questions. Class discussion will be highly encouraged. Please never hesitate to ask the questions. 3

4 The course requires lot of hard work and additional reading. Students should carefully consider this in planning their other courses and activities. Attendance in all the classes is vitally important since class lectures have a close link with each other. VII Evaluation process A. Methods: Class attendance is required. All students are expected to attend. No student is expected to disrupt class. Students will be evaluated based on their performance in examinations (including comprehensive mid term and final examinations), quizzes, homework, and class participation. The details are as follows: Attendance at Lectures: Students are responsible for everything covered in lecture, even if it is not in the book. If a student misses a lecture, he/she should obtain notes from another student. Note-taking styles vary widely; therefore, it is imperative that students are not routinely relying for the notes from others. Students are also responsible for announcements made during lecture concerning the content and types of problems to be expected on exams. Examinations: There will be three major tests, a cumulative midterm exam and a cumulative final examination. All students are required to take every test as scheduled. No makeup tests will be given unless arranged for in advance (see more below). The makeup test should be arranged within a week since the original date scheduled. The official excuse is required to take the makeup test. No more than one makeup test per student will be allowed during the semester. Special Projects: There will be group research project presentations. Acceptable excuses are participation in an activity appearing on the university authorized activity list, death or major illness in a student's immediate family, illness of a dependent family member, participation in legal proceedings or administrative procedures that require a student's presence, religious holy days, illness that is too severe or contagious for the student to attend class (to be determined by Health Center or off-campus physician), required participation in military duties. Students must provide adequate documentation for their excuses. In general, only one make-up exam will be scheduled for all for a missed exam. Makeup exams will typically be slightly harder than regular exams. Assignments: Homework assignments are extremely important. They can really make the subject material extremely clear and prepare students for tests. During each class period, homework will be assigned and it is expected that each student will complete it as much as possible. If there are any questions, students can come and see the instructor during conference hours or make an appointment. First several minutes of lecture period will be utilized to answer questions regarding homework assignment. If homework assignments are done regularly and conscientiously students will really benefit from the course a lot. An instructor will able to cover more material in the class and this, in turn, will provide students rewarding experiences in their other courses. B. Grading Method: Grading Scale Three Tests 15% 45% Cumulative Mid-semester Exam 20% Special Project 10% Cumulative Final Exam 25% Total 100% The Final grade will be determined on the basis of total average at the end of the semester. The following is the recommended scale: A Excellent B Above Average C Average D Below Average 4

5 0-59 F Fail The following clause is for students participating in any GSU extra curricula activity. Any student participating in extra curricular activities (example band, football, track, etc. ) must bring signed verification from activity's sponsor/director on or before the third week of school. Notification of scheduled events, that conflict with test or assignment dates, must be given in advance so that test may be rescheduled. Test or assignments may be rescheduled to an earlier date than the scheduled date, but must be completed prior to the next class period. If the student neglects to give early notification a score of Zero (0) will be given for that test or assignments. An official excuse for student participation is required to makeup an assignment. VIII. Resolution of Concern(s) and Problem(s) If you have any concern(s)/problems(s) regarding any aspect of the course, please discuss it FIRST with the instructor AND THEN with the Dept. Head, Dr. Semwogerere, Tel. No , if necessary. Again, if you need accommodation in this class/setting/facility related to a disability, please make an appointment to see your instructor as soon as possible. 5

Syllabus ENGR 190 Introductory Calculus (QR)

Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.