# Technology Requirements This is an online course and the following technological resources are required:

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4 Course Objective: Examine key concepts in logic and basic computations to develop an aptitude for practical mathematics. Basic mathematical skills are useful in real life. For instance, you use these skills to calculate interest owed on your credit card bills, balance a monthly budget, or estimate fuel consumption of a vehicle. Evaluating statements using logic constructs is also a part of mathematical skills that can be very useful for communicating effectively, making predictions, and drawing conclusions. These skills can also be used to make important decisions in life. A thorough knowledge of mathematics is certainly beneficial for many professions in service sectors, business, technology, and educational fields. The strategy of this course is to develop some of these mathematical skills by learning some of the core concepts of reasoning processes; logic statements; systems of numerals, bases, and computational methods; the metric system; numbers and their properties; arithmetic; and geometric sequences. The course covers the following topics: Critical Thinking, Logic, System of Numeration, the Metric System, and Number Theory and the Real Number System. Content Description Notes Syllabus The first learning outcome discusses the various reasoning processes involved in critical thinking and the guidelines for approaching the problems. The second learning outcome discusses how to decipher logic symbols and logic statements, construct truth tables, perform logic operations, and become familiar with reasoning using logic. The third learning outcome discusses the history of numeration, various numbering systems, computations on different base numerals, and other computational methods. The fourth learning outcome discusses metric units for length, mass and temperature, the conversion process, and dimensional analysis. The fifth learning outcome discusses number theory, the numbers and their properties, how the numbers can be used in sequences to formulate patterns, and how these patterns can be used for the study of nature and in other various technological applications. You have maximum responsibility for your learning and involvement in the course. It is important that you review the syllabus and keep up with the course materials and deadlines. Pretest

8 Connectives," you learned how to represent a statement using logic symbols. Here you learn how to evaluate the compound statements using truth tables. Watch this video about truth tables to learn when the logic statements are true. Exercise 2.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Practice skills/problem Solving: 13-17, 37-43, (odd numbers), pp Practice the skills: 17-21, (odd numbers), pp In the video presentation "Truth Tables for Negation, Conjunction, and Disjunction," you learned how to construct a truth table. Now complete this exercise to practice writing symbolic statements and constructing truth tables. Multimedia 2.2 Review Video Chapter 3, Sections 3.4 and 3.5 Reading 2.2 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp ). Boston, Equivalent statements are one of the frequently used logic statements that appear in political rhetoric, advertising claims, and legal documents. Watch this video to learn about these statements and how to use De Morgan's Laws to check whether the statements are equivalent. One of the most important applications of logic is the ability to arrive at a conclusion by analyzing a given set of statements. This is a useful tool in the decision-making process. Read this material for an overview on how to use your knowledge of logic to evaluate statements (or facts) and draw

10 applications (9th ed., pp , ). Exercise 2.3 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp. 155, 161). Boston, Practice skills/problem Solving: 14-19, p. 155 Practice skills/problem Solving: 57, 11, 13, 19, p. 161 loser. Here is a little secret on how to make an irrefutable argument. Read the materials. Then, you apply the same logic construct to your argument as you do to operate circuit systems in your electronics. Now that is cool! Based on the lesson reading "Euler Diagrams and Syllogistic Arguments," complete this exercise to practice using the Euler diagram, writing symbolic statements that represent circuits, and constructing truth tables. Assignment 2.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., p. 168). Boston, MA: Project: 1, p. 168 Based on the reading "Switching Circuits," where you learned the application of logic in analyzing circuits, complete this assignment to demonstrate your mastery in logic gate operation. Learning Outcome 3: System of Numeration Learning Outcome: Develop understanding of number systems and bases, and competency to carry computations across different bases. The Hindu-Arabic number system that we use today is only one of the many systems that have been used in the history of human civilization. Knowledge about systems of numerations, therefore, provides you with good historical perspective. Furthermore, the knowledge of number systems allows you to gain a deeper understanding of mathematics and its fundamentals. Considering the wide application of base numerals (binary, octal, and hexadecimal) in computers and virtually all electronics, knowledge of fundamental mathematics is certainly more rewarding when choosing a career in computer programming, electronics, and other related fields. This topic covers the history of numeration, various numbering systems, computations on different base numerals, and other computational methods.

12 operate on binary, octal, and hexadecimal base numerals. Read this material about these bases and the computations involved in carrying operations from one base of numerals to another. Multimedia 3.1 Review Videos Chapter 4, Sections 4.3 and 4.4 Assignment 3.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications. (9th ed., pp ). Boston, Challenge Problems: 67-71, pp Watch these short demonstration videos to enhance your knowledge of performing computations across bases. Based on the reading "Other Bases" and demonstration videos (Base 16 to Base 10 and Base 2, Base 2 to Base 10, Base 8 to Base 10 conversion, Adding in Base 2, Multiplying in Base 7), complete this assignment to demonstrate your computational skill in other bases. Learning Outcome 4: The Metric System Learning Outcome: Demonstrate competency to work in the metric system. Metric is the standard measurement system used by the scientific community as well as most countries. Outside the United States it is difficult to have any quantitative sense without knowing metric units. For example, distance in most countries is measured in terms of kilometers (km), and temperature is recorded in degrees Celsius. If you are familiar with only the US standard, you would not have a sense of temperature or distance without the understanding of the metric system. In this learning outcome you learn metric units for length, mass, and temperature. You also learn the conversion process and dimensional analysis. Content Description Notes Reading 4.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). The metric system is a standard unit of measurement. All of

13 the research and technology industries, among others, use this system of measurement. Read these pages for an overview of basic terms and conversions in the metric system. Multimedia 4.1 Animation Chapter 8, Section 8.1 Watch the animation video and complete the interactive examples to practice basic terms and conversion in the metric system. Assignment 4.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., p. 462). Boston, MA: Internet / Research Activities: 75, p. 462 This assignment requires you to perform research on the use of the metric system by a company that exports goods. By completing the assignment, you gain knowledge on how often the metric system is used in the business industry and in what capacity. Complete the assignment to gain knowledge on the development of the metric system in Europe. Reading 4.2 Angel, A.R., Abbott, C.D., & Runde, D.C. applications (9th ed., pp ). Boston, In the United States, the preferred unit for weight is pounds, and for temperature it is degrees Fahrenheit. Because other countries use the metric system, a lack of understanding of metric units can be a business or even personal disadvantage. Read this material to learn about the metric measurement system for mass and temperature, and to perform dimensional

14 analysis and unit conversion to, and from, the metric system. Exercise 4.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp. 461, ). Problem Solving: 59, 63-65, p. 461 Practice the Skills: 11-15, 27-30, pp Use your knowledge of the metric system covered in the reading assignment to complete the exercise on unit conversions of mass and temperature. Assignment 4.2 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., p. 477). Boston, MA: Projects: 1, 2, p. 477 Complete this assignment to understand the importance of the metric system in the medical profession. Learning Outcome 5: Number Theory and the Real Number System Learning Outcome: Demonstrate competency in using magnitude in the context of place values, fractions, and numbers written in scientific notation. Numbers were invented primarily for describing the natural world. Today, our technology relies on numbers to operate. From the description of nature to the application in technology, numbers are everywhere! In this learning outcome, you review number theory, study the numbers and their properties, and identify how the numbers can be used in series and sequences to formulate patterns, and how these patterns can be used for the study of nature and other various applications. Content Description Notes Reading 5.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). To call your friends, you select numbers. To watch a different television program, you switch to different channels indexed by numbers. To record your temperature, you use numbers, and the list goes on. Numbers are used in almost everything we do. To study how numbers take

15 on a variety of roles in our lives, read the material on number theory and integer operations. Exercise 5.1 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Practice the Skills: 15, 21, 33, 41, 47, 53, p. 218 Problem Solving: 61, 65, 67, 71, p. 219 Practice the Skills: 7, 11, 19, 21, 23, 33, 43, 51, p. 227 Problem Solving: 71, 73, p. 228 Based on your knowledge of number theory and integers, complete the following exercise on numbers and integer operations. Reading 5.2 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Exercise 5.2 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Practice the Skills: 15, 21, 25, 27-30, 57, 65, 69, 75, pp Problem Solving: (odd numbers), pp Practice the Skills: 9, 13, 15, 27, 31, 35, 43, 47, 57, 65, pp Problem Solving Skills: 79, 85, pp. You might remember using fractions like "¾ cup of flour" from a recipe. These are rational numbers. There are equally important numbers that cannot be written as fractions, for example 2. They are called irrational numbers. Read these pages to learn about rational and irrational numbers, and how to perform arithmetic operations using these numbers. Complete the exercise to practice your skill with rational and irrational numbers, identification, and performing arithmetic operations.

16 Reading 5.3 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Scientific notations are used in many fields of study, and the properties of real numbers are vital in many areas of mathematics, such as algebra. Read these pages to learn about the properties of real numbers, rules of exponents, and scientific notations. Multimedia 5.1 Animation video Chapter 5, Section 5.6 Watch the animation video and complete the interactive examples for practice with rules of exponents and scientific notations. Reading 5.4 Angel, A. R., Abbott, C. D., & Runde, D. C. applications (9th ed., pp , ). Sequences are patterns of numbers, and they can have many applications such as modeling population growth, disease control, and several others. Read this material for an overview of arithmetic, geometric, and Fibonacci sequences. Multimedia 5.2 Animation videos Chapter 5, Section 5.7 Watch these interactive videos and practice your skill on arithmetic and geometric sequences. Discussion 5.1 Fibonacci Sequence The Fibonacci sequence and the related topic of the golden ratio appear in many places in nature and play an important role in geometry, art, and music. A number of studies have tried to explain why the

18 If you score less than 80 points on any competency you will have an opportunity to review the material and re-take the competency Posttest. You may take the Posttest assessment up to three times. If you have not passed the competency in three attempts, you will work with an Academic Coach to determine another method of fulfilling the program requirements in this subject. In order to demonstrate competency, a score of 80 points or higher is required. If the term ends prior to you being able to demonstrate competency you will receive a grade of "I" and be required to complete the remaining competencies in the next term. Content Description Time Value Notes Posttest Measures your competency of learning outcomes through essay, short answer, and multiple choice questions. 180 minutes 100 points

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