QUANTITATIVE REASONING
WITH FUNCTIONS
Case
Studies for QR (2nd Ed, 2012)
Case Studies for Quantitative Reasoning (2nd ed.) by Madison,
Boersma, Diefenderfer and Dingman. A case book of news stories.
Topics: 1) Numbers and Quantities, 2) Percent and % change, 3)
Measurement and Indices, 4) Linear and Exponential growth, 5) Graphical
Interpretation and Production, and 6) Counting, Probability, Odds &
Risk.
Quantitative Literacy: Thinking Between the Lines.
Table of
Contents. 2017 3rd edition. By Crauder
Quantitative Reasoning:
Tools for Today's Informed Citizen
by Alicia Sevilla and Kay Somers (Moravian College). Available
from
Key Publishing,
Springer and
Amazon.
Press
Release
Topics
Section I: Numerical Reasoning
Topic 1: Organizing Information Pictorially Using Charts and Graphs.
Topic 2: Bivariate Data. Topic 3: Graphs of Functions. Topic 4: Multiple
Variable Functions. Topic 5: Proportional, Linear, and Piecewise Linear
Functions. Topic 6: Modeling with Linear and Exponential Functions.
Topic 7: Logarithms and Scientific Notation. Topic 8: Indexes and
Ratings. Topic 9: Personal Finances. Topic 10: Introduction to Problem
Solving.
Section II: Logical Reasoning
Topic 11: Decision Making. Topic 12: Inductive Reasoning. Topic 13:
Deductive Reasoning. Topic 14: Apportionment. Topic 15: More on Problem
Solving.
Section III: Statistical Reasoning
Topic 16: Averages and FiveNumber Summary. Topic 17: Standard
Deviation, Zscore and Normal Distributions. Topic 18: Basics of
Probability. Topic 19: Conditional Probability and Tables. Topic 20:
Sampling and Surveys. Topic 21: More on Decision Making.
The need for
quantitative reasoning courses has never been stronger: Citing a recent
study funded by the Pew Charitable Trusts, the Associated Press reported
in 2006 that more than half of the nation’s students at fouryear
colleges and universities “lack the literacy to handle complex,
reallife tasks” such as understanding credit card offers, balancing
checkbooks, and computing restaurant tips.
Quantitative Reasoning: Tools for Today’s Informed Citizen helps
students connect mathematics in the classroom with applications in the
real world. Through a series of handson activities and explorations,
the text empowers students by teaching them to apply quantitative
reasoning skills to make informed decisions in their daily lives.
Authors Alicia Sevilla and Kay Somers developed this engaging,
activitybased text for students enrolled in an introductorylevel,
problembased general education quantitative reasoning course, often
called Quantitative Reasoning, Quantitative Literacy, Statistical
Reasoning, Statistical Literacy, (Mathematical) Problem Solving, or
Liberal Arts Mathematics. At many colleges and universities, this course
satisfies a general education requirement in quantitative reasoning
Literacy & Mathematics: A Contemporary Approach to Quantitative
Literacy
by Jay P. Abramson
and Mathew A. Isom ,
Arizona State University. (1st ed. 2005). Table of Contents by Chapter
and Page Number

Number Sense.
1 Intro. 2 Geology: Vastness of Time. 4 Astronomy:
Enormity of Space. 10 Time and Again, Number Sense.
15 Set Theory (Welldefined, Cardinal Number, Union, Intersection).
19 World of Numbers (Integer, Rational & Real). 26
Multiplication Principle (Factorial). 28 Permutations and
Combinations.

Probability. 37
Intro. 41 Introduction to Probability, Coincidences
(Conspiracy, Numerology, Sports, Politics). 52 Determining the
Reasonability of the Media Statistics. 57 Probability.
2C Probability: Independent and Dependent Events. 60
Probability Using Counting Theory. 64 The Binomial Probability
Profile. 69 Conditional Probability. 73 Bayes Theorem.
77 Expected Values.

Statistics. 83
Intro. 85 Causation and Correlation. 91 Circle Graphs.
100 Measure of Central Tendency. 105 Standard Deviation and
Normal Distribution (zscore). 113 Standard Deviation.

Rates of Change. 125
Intro: Numerical versus Percentage Growth. 133 Linear
versus Exponential Growth. 135 Linear Models. 148
Exponential Models. 154 Local Rates of Change. 161 World
Population and Sustainability (Logistic Curves and Population
Collapse). 168 Concavity.

Finance. 173 Intro.
174 Effective Rates, Simple Interest, Compound Interest. 181
Compound Interest. 184 Annual Yield. 187 Annuity.
197 Different Payment and Interest Conversion Periods. 198 The
Mortgage Payment Equation.

Geometry. 203 Intro.
204 Two Dimensional Geometric Figures. 210 Three
Dimensional Geometric Figures. 225 Real Estate Math.
228 Trigonometry. 231 Right Triangle Applications.

Logic. 235 Intro.
237 Inductive Reasoning. 241 Deductive Reasoning.
244 Symbolic Logic. 245 Quantifiers. 249
Connectives. 251 Truth Tables (Biconditional, Common
Negations). 257 Arguments. 261 Fallacy.
The Heart of Mathematics: An invitation to effective thinking
(Hardcover)
by
Edward B. Burger,
Michael Starbird.
Key College
Press; 2nd Edition (August 18, 2004).
Book
Description: The Heart of
Mathematics addresses the big ideas of mathematics (many of which are
cutting edge research topics) in a noncomputational style intended to
be both read and enjoyed by students and instructors, as well as by
motivated general readers. It features an engaging, lively, humorous
style full of surprises, games, mindbenders, and all without either
sacrificing good mathematical thought or relying on mathematical
computation or symbols.
The authors
are awardwinning authors, holding awards such as: Distinguished
Teaching Award (Burger, from the Mathematical Association of America);
Chauvenet Prize (the best expository mathematics writer in the world,
Burger, from the MAA) and many others.

Fun and Games (An Introduction
to Rigorous Thought).
1.1 Silly Stories Each with a Moral (Conundrums that evoke
Techniques of Effective Thinking), 1. 2 Nudges (Leading
Questions and and Hints for Resolving the Stories), 1.3 The
Punch Lines (Solutions and Further Commentary), 1.4 From
Play to Power (Discovering Effective Strategies of Thought for
Life).

Number Contemplation.
2.1 Counting (How the Pigeonhole Principle Leads to Precision
Thought Estimation), 2.2 Numerical Patterns in Nature
(Discovering the Beauty of the Fibonacci Numbers), 2.3 Prime
Cuts of Numbers (How the Prime Numbers are the Building Blocks of
All Numbers), 2.4 Crazy Clocks and Checking Out Bars (Cyclical
Clock Arithmetic and Bar Codes), 2.5 Public Secret Codes and
How to Become a Spy (Encrypting Information Using Modular Arithmetic
and Primes), 2.6 The Irrational Side of Numbers (Are There
Numbers Beyond Fractions), 2.7 Get Real (The Point of Decimals
and Pinpointing Numbers on the Real Line).

Infinity. 3.1 Beyond
Numbers (What Does Infinity Mean?), 3.2 Comparing the Infinite
(Pairing Up Collections Via a OnetoOne Correspondence), 3.3
The Missing Member (George Canton Answers: Are Some Infinities
Larger Than Others?), 3.4 Travels Toward the Stratosphere of
Infinities (The Power Set and the Question of the Infinite Galaxy of
Infinities), 3.5 Straightening Up the Circle (Exploring
the Infinite Within Geometric Objects).

Geometric Gems. 4.1
Pythagoras and his Hypotenuse (How a Puzzle Leads to a Proof of One
of the Gems of Mathematics), 4.2 A View of an Art Gallery
(Using Computational Geometry to Place Security Cameras in Museums),
4.3 The Sexiest Rectangle (Finding Aesthetics in Life, Art and Math
Through the Golden Rectangle), 4.4 Smoothing Symmetry
and Spinning Pinwheels (Can a Floor Be Tiled Without Any Repeating
Pattern?), 4.5 The Platonic Solids Turn Amorous (Discovering
the Symmetry and the Interconnections Among the Platonic Solids),
4.6 The Shape of Reality? (How Straight Lines Can Bend in
NonEuclidean Geometries), 4.7 The Fourth Dimension (Can You
See It?).

Contortions of Space.
5.1 Rubber Sheet Geometry (Discovering the Topological Idea of
Equivalence by Distortion), 5.2 The Band that Wouldn't
Stop Playing (Experimenting with the Mŏbius band and Klein Bottle),
5.3 Feeling Edgy? (Exploring Relationships Among Vertices, Edges and
Faces), 5.4 Knots and Links (Untangling Ropes and Rings),
5.5 Fixed Points, Hot Loops and Rainy Days (How the Certainty of
Fixed Points Implies Certain Weather Phenomena).

Chaos and Fractals.
6.1 Images (Viewing a Gallery of Fractals), 6.2 The Dynamics
of Change (Can Change be Modeled by Repeated Applications of Simple
Processes?), 6.3 The Infinitely Detailed Beauty of Fractals
(How to Create Works of Infinite Intricacy Though Repeated
Processes), 6.4 The Mysterious Art of Imaginary Fractals
(Creating Julia and Mandelbrot Sets by Stepping Out in the Complex
Plane), 6.5 Predetermined Chaos (How Repeated Simple Processes
Result in Utter Chaos), 6.6 Between Dimensions (Can the
Dimensions of Fractals Fall between the Cracks?).

Taming Uncertainty.
7.1 Chance Surprises (Some Scenarios Involving Chance that Confound
Our Intuition), 7.2 Predicting the Future in an Uncertain
World (How to Measure Uncertainty Using the Idea of Probability),
7.3 Random Thoughts (Are Coincidences as Truly Amazing as They First
Appear?), 7.4 Down for the Count (Systematically Counting All
Possible Outcomes), 7.5 Collecting Data Rather than Dust (The
Power and Pitfalls of Statistics), 7.6 What the Average
American Has (Different Means of Describing Data), 7.7
Parenting Peas, Twins and Hypotheses (Making Inferences from Data).

Deciding Wisely (Applications
of Rigorous Thinking). 8.1 Great Expectations (Deciding
How to Weigh the Unknown Future), 8.2 Risk (Deciding Personal
and Public Policy), 8.3 Money Matters (Deciding between
Faring Well and Welfare), 8.4 Peril at the Polls (Deciding Who
Actually Wins an Election), 8.5 Cutting Cake for Greedy People
(Deciding How to Allocate Scarce Resources).
Farewell, Acknowledgments (2nd and 1st ed.), Hints and Solutions, Index,
Credits.
"The Heart of Mathematics is easily the best liberalarts math textbook
ever written. The authors really understand which math is really
beautiful and interesting. .. They are pioneers in writing
engagingly about mathematics." Professor David Kennedy, Granville
State College.
[See also
Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty
Ideas by the same authors. Similar topics but a third
the size.]
Environmental Mathematics in the Classroom
by
B. A. Fusaro (Editor),
P. C. Kenschaft (Editor). MAA (1st ed., 2003).
Book
Description:
Environmental Mathematics seeks to marry the most pressing challenge of
our time with the most powerful technology of our time  mathematics.
This book does this at an elementary level and demonstrates a wide
variety of significant environmental applications that can be explored
without resorting to calculus. Environmental Mathematics in the
Classroom includes several chapters accessible enough to be a text in a
general education course, or to enrich an elementary algebra course.
Groundlevel ozone, pollution and water use, preservation of whales,
mathematical economics, the movement of clouds over a mountain range, at
least one population model and a smorgasbord of 'newspaper mathematics'
can be studied at this level and would form a stimulating course. It
would prepare future teachers not only to learn basic mathematics, but
to understand how they can integrate it into other topics that will
intrigue students.
About the
Authors:
Ben Fusaro received his PhD from the University of Maryland. He went on
to be a Professor Mathematics at the University of South Florida. Queens
College (NC) and Salisbury State University. He introduced
"Environmental Mathematics," a liberal arts course, at Salisbury in
1984, and created the Mathematical Modeling Course in 1985. He has been
actively involved in organizing workshops, and increasing awareness in
the area of environmental mathematics.
Pat
Kenschaft's' many former books include "Mathematics for Human Survival,"
a text for quantitative literacy for college students with all its
exercises and examples using numbers from environmental health, and
peace issues, and "Winning Women into Mathematics," published by the
MAA. She received her PhD in functional analysis from the University of
Pennsylvania, and is currently Professor of Mathematics at Montclair
State University.
QUANTITATIVE REASONING
WITH MODELS
Mathematical Thinking and Quantitative Reasoning
Houghton Mifflin Co
by
Richard N. Aufmann (Palomar College),
Joanne S. Lockwood (New Hampshire Community Technical College),
Richard D. Nation (Palomar College) and Daniel K. Clegg (Palomar
College).
(1st ed. 2008).
"Designed for the nontraditional Liberal Arts course,
Mathematical Thinking and Quantitative Reasoning focuses on
practical topics that students need to learn in order to be better
quantitative thinkers and decisionmakers. The author team's
approach emphasizes collaborative learning and critical thinking
while presenting problem solving in purposeful and meaningful
contexts."
CONTENTS

Problem Solving.
1.1 Inductive and Deductive
Reasoning 1.2 ProblemSolving Strategies
1.3 Problem Solving Using Sets

Logic and its Applications
2.1 Logic Statements and Quantifiers
2.2 Truth Tables and Applications
2.3 The Conditional and Related Statements
2.4 Arguments
2.5 Euler Diagrams

Algebraic Models
3.1 FirstDegree Equations and Formulas
3.2 Rate, Ratio, and Proportion
3.3 Percent 3.4 Direct and
Inverse Variation

Measurement and Geometric Models
4.1 The Metric System
4.2 The U.S. Customary System
4.3 Basic Concepts of Euclidean Geometry
4.4 Perimeter and Area of Plane Figures
4.5 Properties of Triangles
4.6 Volume and Surface Area
4.7 Introduction to Trigonometry

Linear Models
5.1 Rectangular Coordinates and Functions
5.2 Properties of Linear Functions
5.3 Finding Linear Models
5.4 Linear Regression and Correlation

Nonlinear Models
6.1 Introduction to Nonlinear Functions
6.2 Exponential Functions
6.3 Logarithmic Functions

The Mathematics of Finance
7.1 Simple Interest
7.2 Compound Interest
7.3 Credit Cards and Consumer Loans
7.4 Stocks, Bonds, and Mutual Funds
7.5 Home Ownership

Probability and Statistics
8.1 Counting Methods
8.2 Introduction to Probability
8.3 Measures of Central Tendency
8.4 Measures of Dispersion
8.5 Measures of Relative Position
8.6 Normal Distributions
8.7 Inferential Statistics

Apportionment and Voting
9.1 Introduction to Apportionment
9.2 Introduction to Voting
9.3 Weighted Voting Systems

The Mathematics of Graphs 10.1 Traveling Roads and Visiting Cities 10.2 Efficient Routes 10.3
Map Coloring and Graphs
Web Appendix: Algebra Review (Available only
online at this textbook's Online Study Center)
Using and Understanding Mathematics: A Quantitative Reasoning
Approach
by Jeffrey O. Bennett,
William L. Briggs (3rd ed. 2004).
From Book News, Inc. "Aimed at students majoring in nonmathematical
fieldsparticularly those who feel some anxiety about maththis
textbook focuses on the practical applications of mathematics in
college, career, and life. Although not remedial in nature, the text
is suitable for students with a wide range of mathematical
backgrounds. The use of critical thinking skills is emphasized
throughout. Topics include, for example, income taxes, statistical
reasoning, mathematics and music, voting theory, and exponential
population growth. Table of Contents (by Chapter)

Principles of Reasoning. 1A The Forces of Persuasion, An Overview of
Common Fallacies, 1B Propositions: The Building Blocks of
Arguments, 1C Arguments: Deductive and Inductive, 1D Analyzing Real Arguments.

Statistical Reasoning. 2A Fundamentals of Statistics, 2B Should
you believe a Statistical Study?, 2C Basic Statistical
Graphs, 2D Graphs in the Media, 2E Causal Connections.

Problems Solving Tools. 3A Using Unit Analysis, 3B Systems of
Standardized Units, 3C The Process of Problem Solving.

Numbers in the Real World. 4A Concepts of Numbers, 4B Uses and
Abuses of Percentages, 4C Putting Numbers in Perspective,
4D Dealing With Uncertainty.

Financial Management. 5A The Power of Compound Interest, 5B
Savings Plans (Annuities), 5C Loan Payments, Credit Cards and
Mortgages, 5D Income Taxes, 5E Investments.

Modeling our World. 6A Functions: The Building Blocks of our
Mathematical Models, 6B Linear Graphs and Modeling, 6C
Formulas as Models

Exponential Growth and Decay.
7A Exponential Astonishment, 7B Doubling Time and Half Life,
7C Exponential Modeling, 7D Real Population Growth.

Probability: Living with the Odds.
8A Principles of Counting, 8B Fundamentals of Probability,
8C Combining Probabilities, 8D The Law of Averages,
8E Probability, Risk and Coincidence

Putting Statistics to Work. 9A Characterizing Data,
9B Linear Regression Models, 9C Statistical Inference,
9D Sample Issues in Statistical Research.

Mathematics and the Arts. 10A Fundamentals of Geometry,
10B Mathematics and Music, 10C Perspective and Symmetry,
10D Proportion and the Golden Ratio, 10E Fractal Geometry.

Discrete Mathematics in Business and
Society. 11A Network Analysis, 11B The
Traveling Salesman Problem, 11C Project Design, 11D Voting. Does the Majority Always Rule?,
11E Theory of Voting.

The Power of Numbers. A few more topics.
12A Balancing the Federal Budget, 12B Energy: Our Future Depends on it,
12C Density and Concentration, 12D Logarithmic Scales: Earthquakes, Sounds and
Acids.
Essentials of Using and Understanding Mathematics: A Quantitative
Reasoning Approach
by Bennett and Briggs (1st ed. 2002). "This premiere text serves the newly emerging
Quantitative Reasoning/Literacy Course, as well as an alternative
approach for Liberal Arts/Survey Math. It provides a legitimate
alternative for nonquantitative majors, helping to reduce math
anxiety and emphasizing practicality. It's the mathematics you
need for college, career, and life. Essentials of Using and
Understanding Mathematics is a condensed version of the full
book [see above]. It is designed for those who see only the "core"
material for their courses."
For All Practical Purposes: Mathematical Literacy in Today's World
by COMAP (1988, 6th ed. 2002) "COMAP  the
Consortium of Mathematics and Its Applications  is a group of
mathematicians and educators dedicated to the improvement in the teaching of
math by demonstrating to students how math is a crucial part of the world
around us. They believe that students must cultivate an understanding
of math  develop mathematical literacy  if they are to succeed in a
society that is increasingly processdriven and where problemsolving skills
are increasingly important."

Part I: Management Science. Ch 1: Street Networks, Ch
2: Visiting Vertices, Ch 3 Planning & Scheduling, Ch 4: Linear
Programming.

Part 2: Statistics, The Science of Data. Ch 5:
Producing Data, Ch 6: Exploring Data, Ch 7: Probability, Ch 8:
Statistical Inference.

Part 3: Coding Information. Ch 9: Identification Numbers, Ch
10: Transmitting Numbers.

Part 4: Social Choice and Decision Making. Ch 11:
Social Choice, The Impossible Dream, Ch 12: Weighted Voting Systems,
Ch 13: Fair Division, Ch 14: Apportionment, Ch 15: Game Theory, The
Mathematics of Competition.

Part 5: On Size and Shape. Ch 16: Growth and Form, Ch
17: Symmetry and Patterns. Ch 18: Tilings.

Part 6: Modeling in Mathematics. Ch 19: Logic and Modeling, Ch
20: Consumer Finance Models.
PreCalculus: Modeling Our World
by COMAP (2001)
Quantitative Reasoning with Algebra
Quantitative Reasoning and the Environment:
Mathematical Modeling in Context
by
Greg Langkamp and
Joseph Hull (1st ed. 2006).
AMATYC talk
Table of Contents:
Part 1: Essential Numeracy.

Chapter 1:
Measurement and Units. Mercury and the Inuit of
Greenland, Measuring, Accuracy and Precision of Measurement,
Estimation and Approximation, Units of Measurement, Unit Conversion,
Compound Units, Units in Equations and Formulas, Unit Prefixes,
Scientific Notation and Order of Magnitude, Powers of 10 and
Logarithms, Logarithmic Scales

Chapter 2:
Ratios and Percentages. Ratios, Normalization, Percentage as
a Type of Ratio, Parts per Thousand, Parts per Million and Parts per
Billion, Percentage as a Measure of Change, Percentage Difference
and Percentage Error, Proportions, Probability, Recurrence Interval.

Chapter 3:
Graphs and Charts. Pie Charts, Bar Charts, Frequency
Histograms, Using Technology: Histograms, Relative Frequency
Histograms, Scatterplots, Using Technology: Scatterplots, Line
Graphs.
Part 2:
Function Modeling

Chapter 4:
Linear Functions and Regression. Modeling with Linear
Functions, Units of Measure in Linear Equations, Dependent versus
Independent Variables, Graphing Linear Equations, Using Technology:
Graphs and Tables, Approximating AlmostLinear Data Sets,
straightedge method, least squares regression, Using Technology:
Linear Regression, The Correlation Coefficient "r", Using
Technology: The Correlation Coefficient, Correlation Fallacies.

Chapter 5:
Exponential Functions and Regression. Exponential Rates and
Multipliers, The General Exponential Model, Finding Exponential
Functions—the More General Case, Solving Exponential Equations,
Doubling Times and HalfLives, Approximating AlmostExponential Data
Sets, straightedge method, least squares regression, Using
Technology: Exponential Regression.

Chapter 6:
Power Functions. Basic Power Functions, Solving Power
Equations, Approximating AlmostPower Law Data Sets, straightedge
method, least squares regression, Using Technology: Power
Regression, Power Law Frequency Distributions, Power Law
Distributions and Fractals, Recurrence Intervals.
Part 3:
Difference Equation Modeling

Chapter 7:
Introduction to Difference Equations. Sequences and Notation,
Modeling with Difference Equations, Linear Difference Equations,
Exponential Difference Equations, Why Use Difference Equations?,
Affine Difference Equations, Using Technology: Difference Equations.

Chapter 8:
Affine Solution Equations and Equilibrium Values. The
Solution Equation to the Affine Model, Equilibrium Values,
Classification of Equilibrium values, Revisiting the Affine Solution
Equation.

Chapter 9:
Logistic Growth, Harvesting and Chaos. Modeling Logistic
Growth with Difference Equations, Logistic Equilibrium Values,
Harvest Models, Periodic Behavior, Chaotic Behavior.

Chapter
10: Systems of Difference Equations. Systems Modeling, Using
Technology: Systems of Difference Equations, Exponential Change and
Stable Age Distributions, What Else Besides Populations?
Part 4:
Elementary Statistics

Chapter
11: Fundamentals of Statistics. Measures of Center and Other
Descriptive Statistics, Weighted Means, Quartiles and the 5 Number
Summary, Boxplots, Using Technology: Finding Descriptive Statistics,
Shape of a Data Set, Using Technology: Histograms, A Skew Formula,
Comparing the Mean and Median, Sampling.

Chapter
12: Standard Deviation. Standard Deviation, Calculating
Position Using Zscores, Outliers, Chebychev's Rule, Normal
Distributions, The Empirical Rule.

Chapter
13: Normal Distribution. The Standard Normal Distribution,
Transformations to Normal, Confidence Intervals.
Book
Description:
An
introductory quantitative math book with an environmental theme. The
emphasis of this text is on analyzing real environmental information and
problems, using mathematics accessible to students with an intermediate
algebra background. Students using this text will develop mathematical
(and environmental) literacy as they model natural processes using
algebraic, graphical and numerical methods, and analyze data
quantitatively to assist in objective decision making.
The textbook
is comprised of 4 principal sections: (1) basic numeracy; (2) function
modeling; (3) difference equation modeling, and; (4) elementary
statistics. Furthermore, this textbook combines both a reform and
traditional approach. Traditional in that each chapter presents
introductory material, worked examples, multiple student problems, and
solutions to odd exercises. It is reform in that it investigates
material through a synthesis of algebraic, graphical, numerical and
verbal approaches.
Explorations in College Algebra
by
Linda Almgren Kime,
Judith Clark,
Beverly K. Michaelson (3rd ed. 2005).
Table of Contents:

Chapter 1:
Making Sense of Data and Functions. 1.1) Describing
SingleVariable Data, 1.2) Describing Relationships between
Two Variables, 1.3) An Introduction to Functions, 1.4) Visualizing
Functions.

Chapter 2:
Rates of Change and Linear Functions. 2.1) Average
Rates of Change, 2.2) Change in the Average Rate of Change,
2.3) The Average Rate of Change is a Slope, 2.4) Putting a
Slant on Data, 2.5) Linear Functions: When Rates of Change are
Constant, 2.6) Visualizing Linear Functions, 2.7)
Finding Graphs and Functions of Linear Equations, 2.8) Special
Cases, 2.9) Constructing Linear Models for Data. An
Extended Exploration. Using U.S. Census Data, Summarizing the
Data: Regression Lines, Interpreting the Regression Lines:
Correlation vs. Causation

Chapter 3:
When Lines Meet: Linear Systems. 3.1) Systems of Linear
Equations, 3.2) Finding Solutions to Systems of Linear
Equations, 3.3) Linear Inequalities: Reading Between the Lines,
3.4) Systems with Piecewise Linear Functions: Tax Plans.

Chapter 4:
The Laws of Exponents and Logarithms: Measuring the Universe,
4.1) The Numbers of Science: Measuring Time and Space, 4.2) Positive
Integer Exponents, 4.3) Negative Integer Exponents, 4.4)
Converting Units, 4.5) Fractional Exponents, 4.6) Orders
of Magnitude, 4.7) Logarithms Base 10.

Chapter 5:
Growth and Decay: An Introduction to Exponential Functions.
5.1) Exponential Growth, 5.2) Linear vs. Exponential
Functions, 5.3) Exponential Decay, 5.4) Visualizing
Exponential Functions, 5.5) Exponential Functions: A Constant
Percentage Change, 5.6) Examples of Exponential Growth and Decay,
5.7) SemiLog Plots of Exponential Functions.

Chapter 6:
Logarithmic Links: Logarithms and Exponential Functions.
6.1) Using Logarithms to Solve Exponential Functions, 6.2) Base e
and Continuous Compounding, 6.3) The natural Logarithm, 6.4)
Logarithmic Functions, 6.5) Transforming Exponential Functions
to Base e, 6.6) Using SemiLog Plots to Construct Exponential
Models for Data.

Chapter 7:
Power Functions. 7.1) The Tension Between Surface Area
and Volume, 7.2) Direct Proportionality: Power Functions with
Positive Powers, 7.3) Visualizing Positive Integer Powers,
7.4) Comparing Power and Exponential Functions, 7.5) Inverse
Proportionality: Power Functions with Negative Integer Powers,
7.6) Visualizing Negative Integer Power Functions, 7.7) Using
Logarithmic Scales to find the Best Functional Model.

Chapter 8:
Quadratics, Polynomials and Beyond. 8.1) An
Introduction to Quadratic Functions, 8.2) Finding the Vertex:
Transformations of Y = X^{2},
8.3) Finding the Horizontal Intercepts, 8.4) The Average
Rate of Change of a Quadratic Function, 8.5), An introduction
to Polynomial Functions, 8.6) New Functions from Old. An
Extended Exploration: The Scientific Method, The FreeFall
Experiment, Collecting and Analyzing Data from a FreeFall
Experiment.
Book Description
Explorations
in College Algebra, 3/e and its accompanying ancillaries are designed to
make algebra interesting and relevant to the student. The text adopts a
problemsolving approach that motivates students to grasp abstract ideas
by solving realworld problems. The problems lie on a continuum from
basic algebraic drills to openended, nonroutine questions. The focus
is shifted from learning a set of discrete mathematical rules to
exploring how algebra is used in the social, physical, and life
sciences. The goal of Explorations in College Algebra, 3/e is to prepare
students for future advanced mathematics or other quantitatively based
courses, while encouraging them to appreciate and use the power of
algebra in answering questions about the world around us.
Explorations
in College Algebra was developed by the College Algebra Consortium based
at the University of Massachusetts, Boston and funded by a grant from
the National Science Foundation. The materials were developed in the
spirit of the reform movement and reflect the guidelines issued by the
various professional mathematics societies (including AMATYC, MAA, and
NCTM).
Quantitative Reasoning: Understanding the Mathematical Patterns of
Nature by Frederick P. Greenleaf (2nd ed., 2000)
To Students:
"This is not a math course in the familiar sense." The purpose of this
course is "to show why mathematics is necessarily the language of
science. The math topics we cover are fairly elementary, but our
use of them is not. In order to understand how scientists think, you
have to learn to think for yourself using the tools that mathematics
provides. This course aims to show how one can take real world
problems, translate them into mathematics, and solve them." "Quantitative
Reasoning explores the mathematical tools you will need to
understand why mathematics became the language of science."
To Instructors: These materials "address the issue of promoting
quantitative literacy among the vast majority of college students who do
not intend to major in mathematics of the sciences. They were also
designed to be a vehicle for enhancing math and science backgrounds of
the nonspecialist K12 teachers in training."

Measuring Things in the
Real World. What is Mathematics? Real World
Measurements: Dealing With Units, The Art of Making Estimates. 
Growth and Decay
Phenomena. Geometric Progressions and Growth, Growth
of Money, Present Value, Exponential & Logarithmic Functions.

How Big is the Sun, How Far
are the Stars? Scaling Transformations, Size & Form,
Angles & Size of the Earth, Measuring the Inaccessible:
Triangulation, Angular Diameter and the Resolving Power of the Eye,
Next Steps in the Cosmic Distance Ladder, Method of Std. Candles.

Intro to Probability and
Statistics: Counting Problems, Mathematical Probability,
Independent Events, Probability vs. Statistics.
Appendix A: Review of Exponent
Laws; Basic Use of Calculators. Appendix B: Useful Data &
Formulas. Appendix C: Answers to Odd Problems.
Quantitative
and Qualitative Reasoning Skills by James F. Burkhart (2nd ed., 1999)

Understanding Numbers
and Magnitudes. Review of Basic Mathematics, The Number
Line, Neat Trick for Adding and Subtracting, Fraction, The Theory of
Bases.

Algebraic Skills. Exponential Notation,
Scientific Notation, Significant Figures, Arithmetic Operations with
Exponentials, The Associative, Distributive and Commutative
Properties, Factoring, Graphing, Another look at Some Functions,
Solving for the Unknown.

Statistics in Everyday Life. An
Overview, Making a Picture of the Data, Statistics, The Normal
Curve, The Standard Normal Curve, Means Testing.

Fun with Logic. Arguments, fallacies,
Converting Statements to Symbols, Truth Tables.
Mathematical Thinking & Quantitative Reasoning
by Linda R. Sons,
Peter J. Nicholls, Joseph B. Stephen (2nd ed. 1998)

Statistics. 1.1
Graphical Presentations of Data, 1.2 Measures of Central Tendency
and Dispersion, 1.3 The Normal Curve, 1.4 Sampling and CountRecount
Technique, 1.5 Probability, 1.6 The Nature of Statistical Testing.

Logical Statements and Arguments. 2.1
Logical Statements, Conjunctions and Disjunctions,
2.2 Implication Statements and Logical Equivalence, 2.3 Valid
Arguments and Logical Fallacies, 2.4 Survey Analysis.

Geometry in Problem Solving. 3.1 Graphical
Solution of polynomial equations and systems of equations, 3.2
Graphical Solution of Systems of Inequalities, 3.3 Spatial
Relationships.

Estimation, Approximation and Judging the
Reasonableness of Answers. 4.1
Review of the algebraic solution of polynomial equations and systems
of linear equations, 4.2 Inequalities  Maxima and Minima, 4.3 The
Function Concept and the Average Rate of Change,
4.4 Sequential Thinking and the Formulation of Algorithms, 4.5 Error
Analysis.

Problem Solving. 5.1 Strategies in
problem Solving, 5.2 Using the Handheld Calculator/Personal
Computer, 5.3 Personal Business Applications, 5.4 Other
Applications.
Appendix. A.1 Chapter Objectives, A.2 Normal Curve
Percentages,
A.3 Random Digit Table, A.4 ChiSquare Probability Distribution, A.5
Formulas, A.6 Algebraic Background, A.7 Calculators,
A.8 Projects..
Mathematics for Life: A Foundation Course for
Quantitative Literacy by Don Pierce, Ed
Wright, Leon Roland (1997)

Literacy. 1.1
Economic Value, 1.2 Social Value, 1.3 Necessary Skills, 1.4 Course
Mechanics, 1.5 Group Dynamics.

Computers & Operating Systems. 2.1
History,
2.2 Computing and Operating Systems.

Learning and Working in Groups. 3.1 What is
Learning?, 3.2 Components of Knowledge, 3.3 Levels of Learning,
3.4 How We Learn, 3.5 Natural Abilities, 3.6 Thinking Skills, 3.7
Learning in Teams, 3.8 Roles within Teams, 3.9 Team Strategies.

Mathematics: A Historical Approach. 4.1
Roots of Civilization, 4.2 Numeral Systems, 4.3 Basic Operations,
4.4 Arithmetic, 4.5 Modern Numeral Systems.

Algebra and Spreadsheets. 5.1 Egyptian
Algebra, 5.2 Babylonian Algebra, 5.3 Greek Algebra, 5.4 Indian
Algebra, 5.5 Language of Algebra, 5.6 Number Systems, 5.7
Spreadsheets, 5.8 Connecting Algebra to Spreadsheets, 5.9
Graphing Functions using Spreadsheets.

Statistics. 6.1 History, 6.2 Statistics Today,
6.3 Descriptive Statistics, 6.4 Statistics: Uses and Abuses.

Apportionment. 7.1 History, 7.2 Basic
Terminology, 7.3 Methods of Apportionment.

Functions and Modeling. 8.1 Basic Units
of Measurement, 8.2 Modeling the Heavens, 8.3 Linear Models, 8.4
Exponential Models, 8.5 Relations and Functions, 8.6 Curve Fitting.

Probability and Inferential Statistics.
9.1 Empirical Probability, 9.2 Games of Chance, 9.3 Binomial
Distribution, 9.4 Normal Distribution, 9.6 Sampling Distribution of
a Statistic, 9.7 Hypothesis Testing, 9.8 Small Samples.

Internet Essentials. 10.1 History, 10.2
Electronic Mail, 10.3 Finding Information on the Web, 10.4 Surfing
Cyberspace, 10.5 Internet Glossary.
Quantitative
Literacy: Course Manual by Gialamos 4th ed (1999) [Out of Print]
Quantitative
Literacy: Mathematics for Citizenship in the 21st Century by Bennett (1996)
[Out of Print]
Quantitative Reasoning: Mathematics for Citizens in the 21st Century
by Bennett, Briggs and Morrow (1996)
Beyond Problem Solving & Comprehension: An Exploration of Quantitative
Reasoning, Whimbey & Lochhead (1984)
Mathematics for your world: The application of quantitative reasoning to
daytoday problems by
Growney (1982)
MODERN MATHEMATICS / MATH FOR LIBERAL ARTS
CollegeAlgebra Based/Focused
Understanding
our Quantitative World
by Janet Anderson and Todd Swanson (1st ed. 2004).
Preface and Detailed Table of Contents
The perfect
text for a general education mathematics course.
This text is
intended for a general education mathematics course. The authors focus
on the topics that they believe students will likely encounter after
college. These topics fall into the two main themes of functions
and statistics. After the concept of a function is introduced and
various representations are explored, specific types of functions
(linear, exponential, logarithmic, periodic, power, and multivariable)
are investigated. These functions are explored symbolically,
graphically, and numerically and are used to describe real world
phenomena. On the theme of statistics, the authors focus on different
types of statistical graphs and simple descriptive statistics. Linear
regression, as well as exponential and power regression, is also
introduced. Simple types of probability problems as well as the idea of
sampling and confidence intervals are the last topics covered in the
text.
The text is
written in a conversational tone. Each section begins by setting the
mathematics within a context and ends with an application. The questions
at the end of each section are called Reading Questions because students
are expected to be able to answer most of these after carefully reading
the text. Activities and Class Exercises are also found at the end of
each section. These activities are taken from public sources such as
newspapers, magazines, and the World Wide Web. Doing these activities
demonstrates to students that they can use mathematics as a tool in
interpreting quantitative information they encounter outside of the
academy. The course is designed to allow students to spend most of
their time in class working in groups on the activities. Rather than
having students passively listen, this approach requires students to
read, discuss, and apply mathematics. The text assumes that students
will have access to some type of technology such as a graphing
calculator.
Table of Contents (by Chapter)
1. Functions, 2. Graphical Representations of Functions, 3.
Applications of Data, 4. Describing Data (Mean, Median and Standard
Deviation), 5. Displaying Data, 6. Multivariable Functions and
Contour Diagrams, 7. Linear Function, 8. Exponential Functions, 9
Exponential Functions, 10. Logarithmic Functions, 11. Periodic
Functions, 12. Power Functions, 13 Probability, 14. Random Samples.
Appendix: Instructions for
the TI83 Graphing Calculator
Excursions in Modern Mathematics by Peter Tannenbaum (5th ed., 2003)
Book Description: "This collection of “excursions” into
modern mathematics is written in an informal, very readable style, with
features that make the material interesting, clear, and easytolearn.
It centers on an assortment of realworld examples and applications,
demonstrating attractive, useful, and modern coverage of liberal arts
mathematics. The book consists of four independent parts, each
consisting of four chapters—1) Social Choice, 2) Management Science, 3)
Growth and Symmetry, and 4) Statistics. For the study of mathematics."
Preface of 1998 edition, "We have made an concerted
effort to introduce the reader to a view of mathematics that is entirely
different from the traditional algebrageometrytrigonometryfinite math
curriculum that so many people have learned to dread, fear and
occasionally abhor. The notion that general education mathematics
must be dull, unrelated to the real world, highly technical and deal
mostly with concepts that are historically ancient is totally unfounded.
Applicability: The connection between the mathematics presented
here and downtoearth, concrete reallife problems is direct and
immediate." Accessibility: We have found Intermediate Algebra to
be an appropriate and sufficient prerequisite. Aesthetics: A
fundamental objective of this book is to develop an appreciation for the
aesthetic elements of mathematics."
Modern Mathematics by Ruric E. Wheeler, Ed R.
Wheeler (2001)
Book News: "Emphasizing
problemsolving skills, this introductory textbook contains 14 chapters
covering: critical thinking; logic; sets, relations, and functions;
whole numbers and numeration; integers and number theory; rational
numbers; real numbers; consumer mathematics; probability; statistics;
informal geometry; measurement and the metric system; transformations;
and algebra, geometry, and graph theory."
The Mathematical Tourist : New and Updated Snapshots of Modern
Mathematics by Ivars Peterson
(1998/1988)
Modern Mathematics for Elementary School Teachers
by Ruric E. Wheeler, Ed R. Wheeler (9th
ed., 1995)
Concepts of Modern Mathematics
by Ian Stewart (1995)
MATHEMATICS FOR THE
LIBERAL ARTS
Mathematics for Liberal Arts by Richman, Walker, Wisner, Brewer (4th
ed., 2002)
Back Cover: "This book communicates the spirit of
mathematics by means of simple ideas and problems, emphasizing
exploration rather than drill. Its accessible approach encourages
appreciation of mathematics and is ideal for readers with weak
backgrounds, yet is interesting enough to involve anyone. Counting.
Probability. Statistics. Geometry. Logic. Exponential Growth. Averages.
Natural Numbers. Changing Bases. Clock Arithmetic. Secret Writing.
Infinite Sets. Number Theory Selections. For anyone who needs to learn
or review basic math concepts."
Mathematics: A Liberal Arts Approach by Irving
Allen Dodes (2000)
Mathematics for
the Liberal Arts Student by Wisner, Walker Brewer, Richman (1st
ed., 1999)
Mathematics for the Liberal Arts II by Miller, Heeren, et al. (1999)
Mathematics for the Liberal Arts I by Charles D.
Miller, Vern E. Heeren, E. John Hornsby (1999)
Math for Liberal Arts by
Richman (1998)
Mathematics: One of the Liberal Arts by Thomas
J. Miles, Douglas W. Nance (1st ed., 1997)
Book Description: "This text
includes a history of math and covers logic, computing, finance, and
geometry. The numerous exercise and problem sets, including writing
exercises, provide nonmajors with a thorough foundation of
mathematics."
Liberal arts mathematics by Joseph Newmark
(1992*)
A Mathematics Sampler: Topics for the Liberal Arts
by William P. Berlinghoff, Kerry E. Grant (3rd ed., 1992*)
Instructors Guide to Math Liberal Arts
by Johnny Lott, Richard Billstein (1986*)
FUNDAMENTAL CONCEPTS OF MATHEMATICS
Pathways to College
Mathematics.
Table
of Contents (2020) By D. Franklin Wright
Introduction to Mathematical Thinking : The Formation of Concepts in
Modern Mathematics (Popular Science) by
Friedrich Waismann (2003; reproduction of 1959 edition)
Foundations and Fundamental Concepts of Mathematics by Howard
Whitley Eves (3rd ed., 1997)
* Special Order or Out Of Print/Limited Availability. 