Vole Press

Books in print

Essential Advanced Precalculus

A Self-Teaching Guide

by Tim Hill

Can a set be a member of itself? How do we know that the square root of 2 is irrational? Can a graph really represent a function accurately? Is a function just a rule? Does canceling (crossing out) terms mask important algebraic properties? This entirely practical book is for the student who wants a complete command of the prerequisite material on the first day of calculus class. Success in calculus depends on having a reasonable command of all that went before, yet most precalculus students are taught only simple tools and techniques, leaving them with a superficial understanding of problem-solving. Tim Hill explains why things are true and encourages students to go beyond merely memorizing ways of solving a few problems to pass exams.

Book highlights

Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats the subject as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Provides exceptional preparation for a calculus course.
Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. Sets
2. The Real Number System
3. Functions
4. Graphs
5. Solutions

Buy the paperback (amazon.com), 172 pages, cross-referenced to page numbers, indexed

Essential Algebra

A Self-Teaching Guide

by Tim Hill

This no-nonsense guide provides students and self-learners with a clear and readable study of algebra’s most important ideas. Tim Hill’s distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few weeks what conventional schools stretch into months.

Book highlights

Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats algebra as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Covers all the algebra needed to take a calculus course.
Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. A Few Basics
2. Exponents
3. Polynomials
4. Factoring
5. Linear & Quadratic Equations
6. Inequalities & Absolute Values
7. Coordinates in a Plane
8. Functions & Graphs
9. Straight Lines
10. Circles
11. Parabolas
12. Types of Functions
13. Logarithms
14. Dividing Polynomials
15. Systems of Linear Equations
16. Geometric Progressions & Series
17. Arithmetic Progressions
18. Permutation & Combinations
19. The Binomial Theorem
20. Mathematical Induction
21. Solutions

Buy the paperback (amazon.com), 104 pages, cross-referenced to page numbers, indexed

The Essential Calculus Workbook: Limits and Derivatives

by Tim Hill

Ready to step up your game in calculus? This workbook isn’t the usual parade of repetitive questions and answers. Author Tim Hill’s approach lets you work on problems you enjoy, rather than through exercises and drills you fear, without the speed pressure, timed testing, and rote memorization that damage your experience of mathematics. Working through varied problems in this anxiety-free way helps you develop an understanding of numerical relations apart from the catalog of mathematical facts that’s often stressed in classrooms and households. This number sense, common in high-achieving students, lets you apply and combine concepts, methods, and numbers flexibly, without relying on distant memories.

Book highlights

Solutions to basic problems are steeped in the fundamentals, including notation, terminology, definitions, theories, proofs, physical laws, and related concepts.
Advanced problems explore variations, tricks, subtleties, and real-world applications.
Problems build gradually in difficulty with little repetition. If you get stuck, then flip back a few pages for a hint or to jog your memory.
Numerous pictures depicting mathematical facts help you connect visual and symbolic representations of numbers and concepts.
Treats calculus as a problem-solving art requiring insight and intuitive understanding, not as a branch of logic requiring careful deductive reasoning.
Discards the common and damaging misconception that fast students are strong students. Good students aren’t particularly fast with numbers because they think deeply and carefully about mathematics.
Detailed solutions and capsule reviews greatly reduce the need to cross reference a comprehensive calculus textbook.

Table of contents

1. The Slope of the Tangent Line
2. The Definition of the Derivative
3. Velocity and Rates of Change
4. Limits
5. Continuous Functions

Topics covered

The tangent line
Delta notation
The derivative of a function
Differentiable functions
Leibniz notation
Average and instantaneous velocity
Speed
Projectile paths
Rates of change
Acceleration
Marginal cost
Limits
Epsilon-delta definition
Limit laws
Trigonometric limits
Continuity
Continuous functions
The Mean Value Theorem
The Extreme Value Theorem
The Intermediate Value Theorem
Fermat’s theorem

Prerequisite mathematics

Elementary algebra
Real numbers
Functions
Graphs
Elementary trigonometry

Buy the paperback (amazon.com), 64 pages, cross-referenced to page numbers, indexed

The Essential Calculus Workbook: Trigonometric Functions

by Tim Hill

Book highlights

Solutions to basic problems are steeped in the fundamentals, including notation, terminology, definitions, theories, proofs, physical laws, and related concepts.
Advanced problems explore variations, tricks, subtleties, and real-world applications.
Problems build gradually in difficulty with little repetition. If you get stuck, then flip back a few pages for a hint or to jog your memory.
Numerous pictures depicting mathematical facts help you connect visual and symbolic representations of numbers and concepts.
Treats calculus as a problem-solving art requiring insight and intuitive understanding, not as a branch of logic requiring careful deductive reasoning.
Discards the common and damaging misconception that fast students are strong students. Good students aren’t particularly fast with numbers because they think deeply and carefully about mathematics.
Detailed solutions and capsule reviews greatly reduce the need to cross reference a comprehensive calculus textbook.

Table of contents

1. Review of Trigonometry
2. Elementary Trigonometry
3. Derivatives of Sine and Cosine
4. Integrals of Sine and Cosine
5. Derivatives of Other Trigonometric Functions
6. Inverse Trigonometric Functions
7. Harmonic Motion
8. Hyperbolic Functions

Topics covered

Basic trigonometry
Limits, derivatives, integrals, and graphs of basic and inverse trigonometric functions
Solids of revolution
Buffon’s needle problem
The corridor problem
Simple harmonic motion
Newton’s second law of motion
The hyperbolic functions sinh, cosh, and tanh
Catenaries

Prerequisite mathematics

Tangent lines
Curve sketching
Limits
Continuity
Basic derivatives
Basic integrals
Inverse functions
Maxima and minima
Inflection points

Buy the paperback (amazon.com), 100 pages, cross-referenced to page numbers, indexed

Essential Geometry with Analytic Geometry

A Self-Teaching Guide

by Tim Hill

This no-nonsense guide provides students and self-learners with a clear and readable study of geometry’s most important ideas. Tim Hill’s distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few days what conventional schools stretch into months.

Book highlights

Covers classical and analytic geometry.
Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats geometry as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Includes problems (with solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. Triangles
2. Circles
3. Cylinders
4. Cones
5. Spheres
6. Analytic Geometry
7. Solutions
8. Geometry Cheat Sheet

Buy the paperback (amazon.com), 118 pages, cross-referenced to page numbers, indexed

Essential Permutations & Combinations

A Self-Teaching Guide

by Tim Hill

The mathematics of counting permutations and combinations is required knowledge for probability, statistics, professional gambling, and many other fields. But counting is hard. Students find it hard. Teachers find it hard. And in the end the only way to learn is to do many problems. Tim Hill’s learn-by-example approach presents counting concepts and problems of gradually increasing difficulty. If you become lost or confused, then you can back up a bit for clarification. With practice, you’ll develop the ability to decompose complex problems and then assemble the partial solutions to arrive at the final answer. The result: learn in a few weeks what conventional schools stretch into months.

Book highlights

Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats counting as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Provides exceptional preparation for probability and statistics courses.
Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. The Sum Rule and Product Rule
2. Permutations
3. Combinations
4. The Binomial Theorem
5. Combinations with Repetition
6. Summary and Solutions

Buy the paperback (amazon.com), 88 pages, cross-referenced to page numbers, indexed

Essential Precalculus

A Self-Teaching Guide

by Tim Hill

This no-nonsense guide provides students and self-learners with a clear and readable study of the most important ideas of precalculus mathematics. Tim Hill’s distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few weeks what conventional schools stretch into months.

Book highlights

Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats the subject as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Provides exceptional preparation for a calculus course.
Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. The Real Line and Coordinate Plane
2. Straight Lines
3. Circles and Parabolas
4. Functions
5. Graphs
6. Trigonometry
7. Solutions

Buy the paperback (amazon.com), 156 pages, cross-referenced to page numbers, indexed

Essential Trigonometry

A Self-Teaching Guide

by Tim Hill

This no-nonsense guide provides students and self-learners with a clear and readable study of trigonometry’s most important ideas. Tim Hill’s distraction-free approach combines decades of tutoring experience with the proven methods of his Russian math teachers. The result: learn in a few days what conventional schools stretch into months.

Book highlights

Teaches general principles that can be applied to a wide variety of problems.
Avoids the mindless and excessive routine computations that characterize conventional textbooks.
Treats trigonometry as a logically coherent discipline, not as a disjointed collection of techniques.
Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking.
Omits digressions, excessive formalities, and repetitive exercises.
Covers all the trigonometry needed to take a calculus course.
Includes problems (with all solutions) that extend your knowledge rather than merely reinforce it.

Table of contents

1. A Few Basics
2. Radian Measure
3. The Trig Functions
4. Trig Values for Special Angles
5. Graphs of Trig Functions
6. The Major Formulas
7. Inverse Trig Functions
8. The Law of Cosines (and Sines)
9. Solutions
10. Trig Cheat Sheet

Buy the paperback (amazon.com), 74 pages, cross-referenced to page numbers, indexed

Excel Pivot Tables

All editions

by Tim Hill

The jargon associated with Microsoft Excel’s pivot tables (“n-dimensional cross tabulations”) makes them look complex, but they’re really no more than an easy way to build concise, flexible summaries of long lists of raw values. If you’re working with hundreds (or hundreds of thousands) of rows, then pivot tables are the best way to look at the same information in different ways, summarize data on the fly, and spot trends and relationships. This handy guide teaches you how to use Excel’s most powerful feature to crunch large amounts of data, without having to write new formulas, copy and paste cells, or reorganize rows and columns. You can download the sample workbook to follow along with the author’s examples.

Book highlights

Create pivot tables from worksheet databases.
Rearrange pivot tables by dragging, swapping, and nesting fields.
Customize pivot tables with styles, layouts, totals, and subtotals.
Combine numbers, dates, times, or text values into custom groups.
Calculate common statistics or create custom formulas.
Filter data that you don’t want to see.
Create and customize pivot charts.
Unlink a pivot table from its source data.
Control references to pivot table cells.

Table of contents

1. Pivot Table Basics
2. Nesting Fields
3. Grouping Items
4. Calculations and Custom Formulas
5. Filtering Data
6. Charting Pivot Tables
7. Tricks with Pivot Tables

Download the spreadsheet file (1643K zip file)

Buy the paperback (amazon.com), 72 pages, cross-referenced to page numbers, indexed

Get Out of Debt With Math!

Avoiding, Negotiating, and Paying Down Debt the Smart Way

by Tim Hill

This entirely practical guide teaches you the most important aspects of loans, interest rates, credit, savings, and investments. Using high-school mathematics, Tim Hill provides clear and readable lessons that you can use to understand, avoid, negotiate, renegotiate, and pay down your debts. The result: a strong grasp of basic financial concepts, including cash flows, timing issues, the time value of money, and compound interest.

Book highlights

Stresses fundamentals and hard numbers, without the purposeless feel-good filler of conventional personal-finance books.
Conveys insight and removes doubt as to how your debts and savings will change over time.
Encourages the precise logical thinking needed to deal shrewdly and confidently with creditors and banks.
Explains the monstrous power of compound interest, the root cause of the pain of excessive debt.
Teaches general principles that can be applied to a wide variety of financial products, including mortgages, student loans, credit-card debt, leases, car payments, medical expenses, annuities, retirement funds, and stock purchases.
Includes examples that extend your knowledge rather than merely reinforce it, while avoiding empty and excessive routine computations.
Treats financial mathematics as a logically coherent discipline, not as a disjointed collection of techniques.
Reviews the necessary mathematics.
For more-advanced readers, the tools of elementary calculus are used to prove results, solve equations, and derive optimal values.

Table of contents

Introduction
1. Interest
2. Present Value
3. Annual Percentage Rate
4. Mortgages
5. Annuities
6. Stocks
7. Personal Savings
8. Student Loans
9. Kelly Strategy
10. Mathematics Review

Buy the paperback (amazon.com), 74 pages, cross-referenced to page numbers, indexed

Learn to Program with JavaScript

A Self-Teaching Guide

by Chris Kennedy

Learn the core ideas and skills needed to begin programming in any language on any platform. Author Chris Kennedy uses JavaScript to explore the syntax and semantics of a programming language, and shows you how to write and execute your first program and understand what’s going on under the hood. Along the way, you’ll explore other programming languages, including C, Java, and Python, and learn the reasons to choose one language over another. Each lesson builds on the preceding one, so even if you’ve never written a line of code, you’ll gain enough hands-on experience to be comfortable approaching any language. You can download the source code to follow along with all the examples.

Book highlights

Write source code on Windows, Mac, Linux, or Unix systems.
Make sense of programming jargon and buzzwords.
Understand compiled and interpreted languages.
Compare how code is written in different languages.
Work with numbers, strings, booleans, and other types of data.
Get input from the user.
Explore conditions, loops, variables, and expressions.
Control the structure and the flow of a program.
Use assignment, arithmetic, comparison, and logical operators.
Create and call functions.
Organize your code into independent modules.
Work with arrays and collections.
Adopt a programming style.
Read from and write to files.
Avoid common syntax and logic errors.
Debug your programs.
Use classes, objects, properties, and methods.
Link to libraries of ready-to-run code.
Explore memory management, algorithms, multithreading, and other advanced topics.

Table of contents

1. Programming Basics
2. Writing Your First Program
3. Variables & Data Types
4. Conditional Code
5. Functions
6. More About Strings
7. Arrays
8. Programming Style & Pseudocode
9. Input & Output
10. Errors & Debugging
11. Objects
12. Advanced Topics
13. Next Steps

Download the JavaScript files (43K zip file)

Buy the paperback (amazon.com), 124 pages, cross-referenced to page numbers, indexed

Pay Off Your Mortgage Early With Excel!

Create an Optimal Payoff Plan for Your Income

by Tim Hill

The immense power of compound interest is such that adding a small amount of extra principal to each of your mortgage payments will result in thousands (or tens of thousands) in interest savings over the life of your loan. Using only high-school mathematics, Tim Hill provides clear and readable lessons that you can use to understand and pay down your mortgage by using Microsoft Excel (or any spreadsheet software). This entirely practical guide teaches you how to use worksheet functions, array formulas, data tables, and other spreadsheet features to manage your business and personal finances. You’ll also learn the auxiliary skills needed to create and maintain financial spreadsheets: rounding numbers, date and time arithmetic, summing and counting values, and more. Plenty of examples show you how to use these tools for any type of debt or savings: mortgages, student loans, leases, credit-card debt, car payments, medical expenses, annuities, and retirement funds. You can download the sample workbooks to follow along with the author’s examples and calculations.

Book highlights

Covers all versions of Excel.
Learn about basic financial concepts, including cash flows, timing issues, and the time value of money.
Compute the payments needed to pay off a loan or to meet an investment target.
Separate the interest and principal portions of your mortgage or loan payments for tax purposes.
Convert between the commonly used methods of quoting interest rates.
Create amortization schedules to see how your debts change over time.
Build summary tables to compare loans that have different interest rates, loan amounts, or payment terms.
Derive the true interest rate of your investments or loans, including "interest-free" loans.
See how much time it will take to pay off a loan, meet an investment target, or retire.
Determine how much to invest now to meet a future goal.
Calculate how money will accumulate in your retirement or savings accounts.

Table of contents

Part I — Loans & Mortgages
1. Getting Started with Loans & Mortgages
2. Present Value (PV)
3. Future Value (FV)
4. Payments (PMT)
5. Interest Rates (RATE)
6. Periods (NPER)
7. Interest and Principal Components
8. Converting Interest Rates
9. Loan Amortization Schedules
10. Summarizing Loan Options

Part II — Dates & Times
11. Getting Started with Dates & Times
12. Date & Time Basics
13. Date & Time Functions
14. Date Tricks
15. Time Tricks

Part III — Sums & Counts
16. Getting Started with Sums & Counts
17. Counting Basics
18. Counting Tricks
19. Frequency Distributions
20. Summing Basics
21. Summing Tricks

Download the spreadsheet files (213K zip file)

Buy the paperback (amazon.com), 160 pages, cross-referenced to page numbers, indexed

SQL Database Programming

2024 Update

by Chris Fehily

This book teaches newcomers SQL, the language of databases, and includes examples for the most widely used database systems. In all its editions, this book has sold more than 150,000 copies and is popular with end users, students, data scientists, statisticians, epidemiologists, analysts, app developers, webmasters, and hobbyists. Thorough cross-referencing makes it a useful desktop reference for experienced SQL programmers.

Book highlights

Covers Oracle Database, Microsoft SQL Server, Microsoft Access, IBM Db2 Database, MySQL, PostgreSQL, and Standard SQL.
Hundreds of examples of varied difficulty encourage you to experiment and explore.
Download the sample database and SQL source code to follow along with the examples.
Organize your database in terms of the relational model.
Master tables, columns, rows, and keys.
Retrieve, filter, sort, and format data.
Use functions and operators to transform and summarize data.
Create, alter, and drop database tables.
Answer hard questions by using joins, subqueries, constraints, conditional logic, and metadata.
Create indexes that speed sorts and searches.
Use views to secure and simplify data access.
Insert, update, delete, and merge data.
Execute transactions to maintain the integrity of your data.
Avoid common pitfalls involving nulls.
Troubleshoot and optimize queries.
Learn advanced techniques that extend the power of SQL.

Table of contents

Introduction
1. Running SQL Programs
2. The Relational Model
3. SQL Basics
4. Retrieving Data from a Table
5. Operators and Functions
6. Summarizing and Grouping Data
7. Joins
8. Subqueries
9. Set Operations
10. Inserting, Updating, and Deleting Rows
11. Creating, Altering, and Dropping Tables
12. Indexes
13. Views
14. Transactions
15. Advanced SQL

Read the whole book here, free (html format)

Download the SQL source code (279K zip file)

Create the sample database

Buy the paperback (amazon.com), 466 pages, two-column layout, cross-referenced to page numbers, indexed, front cover, sample chapter (454K pdf file)