Each chapter concludes with a Summary, Research Questions, a
Practice Test, and Answers.
1. PROBLEM SOLVING.
Inductive Reasoning. Estimation: A Problem Solving Tool. Graph
Interpretation: A Problem-Solving Tool.
2. SETS.
Sets: A Problem-Solving Tool. Set Operations. Venn Diagrams. The
Number of Elements in a Set: A Problem-Solving Tool. Infinite
Sets.
3. LOGIC.
Statements. Truth Tables: A Problem-Solving Tool. The Conditional
and the Biconditional. Variations of the Conditional and
Implications. Euler Diagrams: A Problem-Solving Tool. Truth Tables
and Validity Arguments. Switching Networks: A Problem-Solving
Tool.
4. NUMERATION SYSTEMS.
Egyptian, Babylonian, and Roman Numeration Systems. The
Hindu-Arabic (Decimal) System. Number Systems with Bases Other Than
10. Binary Arithmetic. Octal and Hexadecimal Arithmetic.
5. NUMBER THEORY AND THE REAL NUMBERS.
Number Theory: Primes and Composites. Whole Numbers, Integers, and
Order of Operations. The Rational Numbers. Decimals, Scientific
Notation, and Significant Digits. Rationals as Decimals: Percents.
Real Numbers, Square Roots, and Decimal Representation. Radicals.
Number Sequences.
6. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING.
Solutions of First-Degree Sentences. Graphs of Algebraic Sentences.
Sentences Involving Absolute Values. Quadratic Equations. Modeling
and Problem Solving. Ratio, Proportion, and Variation.
7. FUNCTIONS AND GRAPHS.
Graphing Relations and Functions. Linear Functions, Relations, and
Applications. Slopes and Equations of a Line. Quadratic Functions
and Their Graphs. Exponential and Logarithmic Functions. Two Linear
Equations in Two Variables. Linear Inequalities. Linear
Programming.
8. GEOMETRY.
Points, Lines, Planes, and Angles. Triangles and Other Polygons.
Perimeter and Circumference. Area Measure and the Pythagorean
Theorem. Volume and Surface Area. Networks, Non-Euclidean Geometry,
and Topology. Right Triangle Trigonometry. Chaos and Fractals.
9. MATHEMATICAL SYSTEMS AND MATRICES.
Matrix Operations. Solving Systems of Linear Equations with
Matrices. Clock and Modular Arithmetic. Abstract Mathematical
Systems: Groups and Fields. Game Theory.
10. COUNTING TECHNIQUES.
The Sequential Counting Principle (SCP): A Problem-Solving Tool.
Permutations. Combinations. Miscellaneous Counting Methods.
11. PROBABILITY.
Sample Spaces and Probability. Counting Techniques and Probability.
Computation of Probability. Conditional Probability. Independent
Events. Odds and Mathematical Expectation.
12. STATISTICS.
Sampling and Frequency Distribution. Measures of Central Tendency:
The Mean, Median, and Mode. Measures of Depression: The Range and
Standard Deviation. The Normal Distribution: A Problem Solving
Tool. Statistical Graphs: A Problem-Solving Tool. Making
Predictions: Linear Regression. Scattergrams and Correlation.
13. YOUR MONEY AND YOUR MATH.
Interest, Taxes, and Discounts. Credit Cards and Consumer Credit.
Annual Percentage Rate (APR) and the Rules of 78. Buying a House.
Investing in Stocks, Bonds, and Mutual Funds.
14. VOTING AND APPORTIONMENT. (Online Only)
Voting Systems. Voting Objections. Apportionment Methods.
Apportionment Objections.
15. GRAPH THEORY. (Online Only)
Introduction to Graph Theory. Euler Paths and Euler Circuits.
Hamilton Paths and Hamilton Circuits. Trees.
APPENDIX: THE METRIC SYSTEM. (Online Only)
A.1 Metric Units of Measurement. A.2 Convert If You Must.
Ignacio Bello attended the University of South Florida (USF), where
he earned a B.A. and M.A. in Mathematics. He began teaching at USF
in 1967, and in 1971 he became a member of the faculty and
Coordinator of the Math and Sciences Department ay Hillsborough
Community College (HCC). Professor Bello instituted the USF/HCC
remedial program, which started with 17 students taking
Intermediate Algebra and grew to more than 800 students with
courses covering Developmental English, Reading, and
Mathematics.
In addition to Topics in Contemporary Mathematics, Professor Bello
has written many other books that span the mathematics curriculum,
many of which have been translated to Spanish. Professor Bello is
featured in three television programs on the award-winning
Education Channel. He helped create and develop the USF Mathematics
department website, which serves as support for the Finite Math,
College Algebra, Intermediate Algebra, Introductory Algebra, and
CLAST classes at USF.
Professor Bello is a member of the Mathematical Association of
America (MAA) and the American Mathematical Association of Two-Year
Colleges (AMATYC). He has given many presentations regarding the
teaching of mathematics at the local, state, and national levels.
1. Introduction to Cognitive Psychology. 2. Cognition and the Brain: Basic Principles. 3. Perception. 4. Attention. 5. Short-Term and Working Memory. 6. Long-Term Memory: Basic Principles. 7. Everyday Memory and Memory Errors. 8. Knowledge. 9. Visual Imagery. 10. Language. 11. Problem Solving. 12. Reasoning and Decision Making.
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