The Joy of Finite Mathematics
The Language and Art of Math
- 1st Edition - October 27, 2015
- Latest edition
- Authors: Chris P. Tsokos, Rebecca D. Wooten
- Language: English
The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language… Read more
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Description
Description
The Joy of Finite Mathematics: The Language and Art of Math
teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance.Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas.
The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance.
The book is based on the authors’ experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida’s CLAST exam or similar core requirements.
Key features
Key features
- Highlighted definitions, rules, methods, and procedures, and abundant tables, diagrams, and graphs, clearly illustrate important concepts and methods
- Provides end-of-chapter vocabulary and concept reviews, as well as robust review exercises and a practice test
- Contains information relevant to a wide range of topics, including symbolic language, contemporary math, liberal arts math, social sciences math, basic math for finance, math for humanities, probability, and the C.L.A.S.T. exam
- Optional advanced sections and challenging problems are included for use at the discretion of the instructor
- Online resources include PowerPoint Presentations for instructors and a useful student manual
Readership
Readership
Undergraduate non-science students, foundational content
Table of contents
Table of contents
- A Summary of the Proposed Options
- Abstract
- 1.1 Introduction to Math
- 1.2 What Is Logic?
- 1.3 Usefulness of Sets
- 1.4 Counting Techniques
- 1.5 Probability
- 1.6 Bernoulli Trials
- 1.7 The Bell-Shaped Curve
- 1.8 Statistics
- 1.9 Geometry
- 1.10 Arithmetic and Algebra
- 1.11 Finance
- 1.12 Game Theory
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Abstract
- 2.1 Logic
- 2.2 Statements and Their Truth Values
- Exercises
- 2.3 Truth Tables
- Exercises
- 2.4 Properties of Logic
- Exercises
- 2.5 Variations of the Conditional Statement
- Exercises
- 2.6 Quantified Statement
- Exercises
- 2.7 Negating Statements
- Exercises
- 2.8 Testing the Validity of an Argument
- Exercises
- 2.9 Applications of Logic
- Exercises
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 3.1 Introduction to Set Theory
- 3.2 The Concept of a Set
- Problems
- 3.3 The Algebra of Sets
- Problems
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 4.1 Introduction to Counting
- Problems
- 4.2 Multiplication Principle
- Problems
- 4.3 Permutations and Combinations
- Problems
- 4.4 Other Counting Techniques
- Problems
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 5.1 Introduction to Probability
- 5.2 Definition of Probability
- Exercises
- 5.3 The Sample Space
- Exercises
- 5.4 Computing Probabilities of Events
- Exercises
- 5.5 Laws of Probability
- Exercises
- 5.6 Conditional Probability
- Exercises
- 5.7 Bayes' Rule
- Exercises
- 5.8 Combinatorial Techniques
- Exercises
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 6.1 Introduction to Random Variables
- Problems
- Problems
- Problems
- Problems
- Problems
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 7.1 Introducing Continuous Random Variables
- Problems
- 7.2 Normal Probability Distributions
- Problems
- 7.3 Standard Normal Probability Distributions
- Problems
- 7.4 Normal Approximation to the Binomial
- Problems
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- 8.1 Data Organization
- Exercises
- 8.2 Graphical Representative of Qualitative Information
- Exercises
- 8.3 Graphical Representation of Quantitative Information
- Exercises
- 8.4 Measuring Central Tendencies
- Exercises
- 8.5 Measuring Deviation from the Center
- Exercises
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
- Abstract
- Fundamental Axioms
- Critical Thinking and Basic Exercise
- Summary of Important Concept
- Review Test
- Abstract
- 10.1 Introduction to the Real Number System
- Exercises
- 10.2 Basic Arithmetic
- Exercises
- 10.3 Pattern Recognition
- Exercises
- 10.4 Algebraic Expressions and Relationships
- Exercises
- 10.5 Equations: Equalities & Systems of Equations
- Exercises
- 10.6 Functions: Linear & Quadratic
- Exercises
- Critical Thinking and Basic Exercises
- Summary of Important Concepts
- Review Test
- Abstract
- 11.1 Introduction to Basic Financing
- Exercises
- 11.2 Savings, Sinking Funds, and Amortization
- Exercises
- 11.3 Comparison Shopping
- Exercises
- 11.4 Comparison Using Effective Rates
- Exercises
- 11.5 Personal Finance
- Exercises
- Critical Thinking and Basic Exercises
- Summary of Important Concepts
- Review Test
- Abstract
- 12.1 Introduction to Game Theory
- 12.2 The Matrix Game
- 12.3 Strictly Determined Game: The Saddle Point
- Problems
- 12.4 Games with Mixed Strategies
- Problems
- 12.5 Reducing Matrix Games to Systems of Equations
- Problems
- Critical Thinking and Basic Exercise
- Summary of Important Concepts
- Review Test
Review quotes
Review quotes
"This textbook includes the fundamentals of logic, set theory, combinatorics, probability, statistics, geometry, algebra, finance, and more. Aimed at undergraduate students in social sciences, finance, economics, and other areas, this liberal arts math text is said to be ‘appropriate for preparing students for Florida’s CLAST exam or similar core requirements. […]
This book includes several topics generally not seen in comparable texts. I am very pleased, even impressed, to see that:
- Readers will encounter here an introduction to reasoning through the motivated presentation of basic logic. The use of a truth table to draw conclusions about a statement is a lost art now, rarely taught in secondary education and early college, at least in America. This dovetails nicely with the authors’ electrical switching (parallel and serial) word problems.
- The book includes well-considered personal finance advice, fulfilling a very present need for practical education. It includes bankruptcy laws, savings instruments, insurance types, budgeting, sales tax, and more. Together with a few pages on considering renting versus leasing versus buying, this chapter is strong in the practicalities of personal finance.
- The syntax of proofs, including ∀ and ∃.
- Induction is covered earlier and at greater depth than is typical.
- There is a deeper introduction to statistics, including the normal distribution, z-scores, and a very good introduction to normal approximation for binomial probabilities.
- A decent bit of geometry filling a gap I typically have to deal with by supplementary material, for example to explain "scalene"and the implication of an axis being "transverse."
- Set theory that goes deeper than usual, for instance reaching to "closure", etc. […]
The authors’ choices of what to include and exclude mean this book may not match a typical curriculum. I see this book as containing enough for perhaps two semesters of first-year college coursework."—Excerpted from the Mathematical Association of America (MAA) review by Tom Schulte, 01/11/2017. Professor Shulte teaches finite mathematics and algebra courses at Oakland Community College in Michigan.
Product details
Product details
- Edition: 1
- Latest edition
- Published: November 5, 2015
- Language: English
About the authors
About the authors
CT
Chris P. Tsokos
Chris P. Tsokos is Distinguished University Professor of Mathematics and Statistics at the University of South Florida. Dr. Tsokos’ research has extended into a variety of areas, including stochastic systems, statistical models, reliability analysis, ecological systems, operations research, time series, Bayesian analysis, and mathematical and statistical modelling of global warming, both parametric and nonparametric survival analysis, among others. He is the author of more than 400 research publications in these areas, including Random Integral Equations with Applications to Life Sciences and Engineering, Probability Distribution: An Introduction to Probability Theory with Applications, Mainstreams of Finite Mathematics with Applications, Probability with the Essential Analysis, Applied Probability Bayesian Statistical Methods with Applications to Reliability, and Mathematical Statistics with Applications, among others. Dr. Tsokos is the recipient of many distinguished awards and honors, including Fellow of the American Statistical Association, USF Distinguished Scholar Award, Sigma Xi Outstanding Research Award, USF Outstanding Undergraduate Teaching Award, USF Professional Excellence Award, Pi Mu Epsilon, election to the International Statistical Institute, Sigma Pi Sigma, USF Teaching Incentive Program, and several humanitarian and philanthropic recognitions and awards. He is also serves as Honorary Editor, Chief-Editor, Editor or Associate Editor for more than twelve academic research journals. Dr. Tsokos is the inventor or co-inventor recipient of several U.S. patents in cybersecurity and health sciences.
Affiliations and expertise
Distinguished University Professor of Mathematics and Statistics, University of South Florida, USARW
Rebecca D. Wooten
Rebecca D. Wooten is Assistant Professor of Mathematics and Statistics at the University of South Florida. In 15 years of teaching, she has been recognized for her excellence in teaching courses such as Liberal Arts Math, Basic Statistics, Introduction to Statistics and Applied Statistics Methods. Her research interests are concentrated in Applied Statistics with emphasis on Environmental Studies. Professor Wooten is extensively involved in activities to improve education not only in Mathematics and Statistics, but Education in general. She is the Academic Coordinator for two free-educational assistance program which offer opportunities for students to volunteer and the local community to get the assistance in their studies that they would have otherwise been unable to afford.
Affiliations and expertise
University of South Florida, Tampa, FL, USAView book on ScienceDirect
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