MATH 0015. Discrete Mathematics

Units: 4
Prerequisite: Completion of MATH 30 with grade of "C" or better
Hours: 72 lecture
Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction. (CSU, UC)

MATH 0015 - Discrete Mathematics

http://catalog.sierracollege.edu/course-outlines/math-0015/

Catalog Description Prerequisite: Completion of MATH 30 with grade of "C" or better Hours: 72 lecture Description: Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction. (CSU, UC) Course Student Learning Outcomes CSLO #1: Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. CSLO #2: Construct valid proofs of theorems using the following techniques: mathematical induction, direct and indirect proofs, by contradiction, with truth tables, and by logical equivalences. CSLO #3: Solve counting problems using combinatorics, recurrence relations, and generating functions. CSLO #4: Solve applied problems using discrete probability theory, graph theory, tree diagrams, and Boolean Algebra. Effective Term Fall 2021 Course Type Credit - Degree-applicable Contact Hours 72 Outside of Class Hours 144 Total Student Learning Hours 216 Course Objectives 1. Create mathematical proofs directly, indirectly, and by contradiction; 2. Use mathematical induction to create a mathematical proof; 3. Create a mathematical proof with truth tables and logical equivalences; 4. Translate mathematical statements using universal and existential quantifiers; 5. Use sets to organize and quantify data; 6. Create an algorithm using pseudocode; 7. Evaluate a series; 8. Model using permutations and combinations and numerically evaluate appropriate applied problems; 9. Model using probabilities, including conditional probabilities; 10. Solve counting problems using a generating function; 11. Assess that a relation is an equivalence relation; 12. Create a graph and a tree to describe the structure of a system; 13. Use Boolean algebra to mathematically model electronic circuits; 14. Verify functions are one-to-one and onto; 15. Use matrices to solve applied problems. General Education Information Approved College Associate Degree GE Applicability AA/AS - Comm & Analyt Thinking AA/AS - Mathematical Skills CSU GE Applicability (Recommended-requires CSU approval) CSUGE - B4 Math/Quantitative Reasoning Cal-GETC Applicability (Recommended - Requires External Approval) IGETC Applicability (Recommended-requires CSU/UC approval) IGETC - 2A Math/Quan Reasoning Articulation Information CSU Transferable UC Transferable Methods of Evaluation Classroom Discussions Example: A classroom discussion will be employed upon the completion of a presentation from a student, particularly with an example of proof writing. The instructor will assess the rigor, clarity, and correctness of the proof. In addition, the instructor will assess the level of understanding of the student presenting such a proof through that student's answers to questions from other students and from the instructor. Objective Examinations Example: Exams will determine a student's ability to independently construct a mathematical proof. For example, a student might be asked to write a formal proof that sqr(2) is irrational. The instructor will assess the success of the proof by determining if the appropriate proof format is used (i.e., proof by contradiction), that the guidelines of such a proof are being employed (i.e., the negation of the conclusion of the conditional statement in the theorem is stated), and that the remaining body of the proof meets college level rigor and clarity. Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: The instructor will provide through a lecture format mathematical proofs of various types, including proof by contradiction. The instructor will then ask the student to construct a proof of this type. An example is: prove that sqr(2) is irrational. Typically, a student will provide his/her proof to the class and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation. (Objective 1) The instructor will provide through a lecture format mathematical proofs of various types, including mathematical induction. The instructor will then ask the student to construct a proof of this type. An example is: prove that the sum of the first n integers is n(n+1)/ Typically, a student will provide his/her proof to the class and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation. (Objective 2) Distance Learning The instructor will provide through a lecture format mathematical proofs of various types, including proof by contradiction. The instructor will then assign the student to construct a proof of this type. An example is: prove that sqr(2) is irrational. Typically, a student will post his/her proof to the class discussion board and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation. (Objective 1) The instructor will provide through a lecture format mathematical proofs of various types, including mathematical induction. The instructor will then assign the student to construct a proof of this type. An example is: prove that the sum of the first n integers is n(n+1)/ Typically, a student will post his/her proof to the class discussion board and both students and instructor will evaluate the correctness, the level of rigor, and the clarity of presentation. (Objective 2) Typical Out of Class Assignments Reading Assignments 1. Throughout the course, read assigned topics from text. For example, how to verify the validity of a mathematical formula by mathematical induction. Students should be prepared to discuss in class. 2. Search the library or the internet for applications of the golden ratio and the Fibonacci sequence and be prepared to discuss in class. Writing, Problem Solving or Performance 1. Write mathematical proofs. For example, given a function f, prove that the image of the intersection of two sets is a subset of the intersection of the images of those two sets. 2. Prove that the limit of the ratio of a Fibonacci number to its predecessor is the golden ratio. Other (Term projects, research papers, portfolios, etc.) Required Materials Discrete Mathematics and Its Applications Author: Kenneth Rosen Publisher: McGraw Hill Publication Date: 2019 Text Edition: 8th Classic Textbook?: No OER Link: OER: Discrete Mathematics with Applications Author: Susanna Epp Publisher: Cengage Publication Date: 2020 Text Edition: 5th Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course.

SOC 0015 - Introduction to Statistics in Sociology

http://catalog.sierracollege.edu/course-outlines/soc-0015/

Catalog Description Prerequisite: Completion of intermediate algebra or appropriate placement Advisory: Concurrent enrollment in a support course (SOC 15S or SOC 815S) is strongly recommended for those who have not recently completed intermediate algebra Hours: 54 lecture Description: Introduction to the use of descriptive and inferential statistics in the analysis of sociological data, including: levels and types of measurement, measures of central tendency and variability, distributions, probability, estimation, hypothesis testing, correlation, and regression. Social science statistical software will be explored as an aid in processing and analyzing sociological data. (C-ID SOCI 125) (CSU, UC-with unit limitation) Course Student Learning Outcomes CSLO #1: Conduct statistical analysis of sociological data. CSLO #2: Interpret and critically analyze the results of statistical analysis. CSLO #3: Organize, classify, and display sociological data in various forms. CSLO #4: Demonstrate familiarity with utilizing statistical software to analyze sociological data. Effective Term Fall 2024 Course Type Credit - Degree-applicable Contact Hours 54 Outside of Class Hours 108 Total Student Learning Hours 162 Course Objectives 1. Practice mathematical techniques and apply them to social science data; 2. Conduct numerical computations; interpret and critically analyze the results in written form; 3. Organize, classify, and represent quantitative data in various forms: tables, graphs, rates, percentages, measures of central tendency and variability; 4. Make statistical inference using estimation, hypothesis testing, correlation, and regression; 5. Demonstrate familiarity with applications in statistical software. General Education Information Approved College Associate Degree GE Applicability AA/AS - Comm & Analyt Thinking AA/AS - Mathematical Skills CSU GE Applicability (Recommended-requires CSU approval) CSUGE - B4 Math/Quantitative Reasoning Cal-GETC Applicability (Recommended - Requires External Approval) IGETC Applicability (Recommended-requires CSU/UC approval) IGETC - 2A Math/Quan Reasoning Articulation Information CSU Transferable UC Transferable Methods of Evaluation Essay Examinations Example: Discuss the pros and cons of using the mean as a measure of central tendency for the above question. Would you choose to report the mean or the median for the above set of data? Why? (This essay refers to the same set of data included in the Problem Solving Example.) Objective Examinations Example: Both stepwise regression and hierarchical regression involve adding variables to a multiple regression equation one step at a time and checking whether the addition significantly improves the prediction. Which of the following statements about the two procedures is true? a) Stepwise regression is more useful than hierarchical regression in exploratory research where one doesn't know what to expect. b) Hierarchical regression is more useful than stepwise regression in applied research domains in which one is looking for the best prediction formula without caring about its theoretical meaning. c) In stepwise regression, the order in which the variables are added is based on some theory or plan, decided in advance by the researcher. d) In hierarchical regression, the computer figures out the best variables to add until adding more makes no additional significant contribution. Problem Solving Examinations Example: Calculate the mode, mean, and median for the following responses on a survey asking how people feel about raising property taxes to pay for improvements at a local community college (5 indicates strongly in favor, 1 indicates strongly not in favor). Data set: 5 4 3 5 1 1 1 1 1 2 2 5 3 1 1 2 2 2 1 5 Skill Demonstrations Example: Using SPSS and the General Social Survey, determine whether there is a statistically significant difference in self-reports of poor mental health during the past 30 days comparing males to females (MNTLHLTH and SEX). Repeatable No Methods of Instruction Lecture/Discussion Distance Learning Lecture: Instructor will provide a lecture about measures of variability and demonstrate how to calculate measures of variability. Then the instructor will provide a practice problem for students to work on in small groups to demonstrate their comprehension of the measures of variability. After a PowerPoint-driven lecture on bivariate analysis, the instructor will walk students through the steps necessary to produce Bivariate Tables on the computers using the SPSS software. At each step, instructor will ask students to respond to questions about why the steps are being taken and what the resulting data tells us. Then the instructor will ask the students to produce a Bivariate Table from a given set of variables on their own to demonstrate they have understood and can replicate the process. Distance Learning Instructor creates a video demonstrating how to perform hypothesis testing and discussing its application in sociological research. As students watch the video, they are encouraged to pause/play at each key step to complete the work on their own along with the instructor so they can become familiar with the process. Typical Out of Class Assignments Reading Assignments 1. Prior to reading chapter, please read the handout entitled "Overcoming Math Anxiety" by Sheila Tobias. This reading will help with any anxiety you may have about taking a statistics course. 2. Read chapter and the case study by Margaret L. Anderson and Patricia Hill Collins entitled "Race, Class, and Gender" which demonstrates the sampling distributions discussed in chapter. Writing, Problem Solving or Performance Sample Writing and Problem Solving Questions for Assignments or Exams: 1. You listen to a debate between two politicians discussing the economic health of the United States. One politician says that the average household income in the United States is $126,500; the other says that the average household income is only $70,784, so Americans are not as well off as the first politician claims. Is it possible for both of these politicians to be correct? If so, explain how. 2. Using the data about the upcoming election, calculate the 95% Confidence Interval for the proportion of registered voters voting for Candidate A. Is it possible they will lose the election based on this Confidence Interval? Explain your response. 3. Regular written check-in assignments with students about course content as well as needs outside of class. Other (Term projects, research papers, portfolios, etc.) At the beginning of the semester, students will choose a sociological topic they are interested in and then complete analysis for each statistic they learn throughout the semester. At the end of the semester, students will compile all of their calculations and critical analysis into one cohesive assignment demonstrating their knowledge of sociological statistics and their application to sociological topics. Required Materials Social Statistics for a Diverse Society Author: Chava Frankfort-Nachmias and Anna Leon Guerrero Publisher: Sage Publication Date: 2020 Text Edition: 9th Classic Textbook?: No OER Link: OER: Elementary Statistics in Social Research: Essentials Author: Jack A. Levin and James Alan Fox Publisher: Pearson Publication Date: 2019 Text Edition: 4th Classic Textbook?: No OER Link: OER: Statistics for the Behavioral and Social Sciences: A Brief Course Author: Arthur Aron, Elliot Coups, and Elaine Aron Publisher: Pearson Publication Date: 2021 Text Edition: 6th Classic Textbook?: No OER Link: OER: Statistics: A Tool for Social Research and Data Analysis Author: Joseph F. Healey and Christopher Donoghue Publisher: Cengage Publication Date: 2021 Text Edition: 11th Classic Textbook?: No OER Link: OER: Other materials and-or supplies required of students that contribute to the cost of the course. SPSS software

Course Identification Numbering System (C-ID)

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...0142 MATH 120 MATH 0019 MATH 140 MATH...0270 BUS 140 IT 0015 CDEV 100 HDEV...

Information Technology

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...Business Applications 3 IT 0015 Business Information Systems...for Many Uses 3 MATH 0013 Elementary Statistics...

Administration of Justice

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...Introduction to Sociology SOC 0015 Introduction to Statistics in Sociology or MATH 0013 Elementary Statistics...