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Self-Guided Courses

"It's impossible to fall behind in a self-guided course."

Statistics have shown that even with increased emphasis on the concept of no-child-left-behind, too many students enter college at the remedial level in mathematics. Essentially such students "waste" part of their first college year studying subjects that should have been mastered previously. If you tend to have difficulty with arithmetic or algebra our courses can be the answer to your entering college without having to do remedial work. If you are in high school and struggling with pre-calculus or higher-level courses, it is likely due to not properly internalizing arithmetic and basic algebra.

Taking advantage of our courses can be the answer for you!

Arithmetic -- Gateways to Mathematics

Our Arithmetic course, developed by Professor Herb Gross and titled 'Gateways To Mathematics' (GTM), has 4 components:

1. Videotaped Lectures

For most people viewing a lecture is easier to internalize than reading a traditional textbook. Our videos are in lock-step with textbook material.

  1. Preface
  2. Module 1: The Development of Place Value
  3. Module 1: Solutions Exercise Set 1
  4. Module 2: Addition and Subtraction of Whole Numbers
  5. Module 2: Solutions Exercise Set 2 Form B
  6. Module 3: Multiplication and Factoring Whole Numbers
  7. Module 3: Solutions Exercise Set 3 Form B
  8. Module 4: Rational Numbers Part 1 Common Fractions
  9. Module 4: Solutions Exercise Set 4 Form B
  10. Module 5: Rational Numbers Part 2 Common Fractions (continued)
  11. Module 5: Solutions Exercise Set 5 Form B
  12. Module 6: Rational Numbers Part 3 Percents and Mixed Numbers
  13. Module 6: Solutions Exercise Set 6 Form B
  14. Module 7: Rational Numbers Part 4 Introduction to Decimal Fractions
  15. Module 7: Solutions Exercise Set 7 Form B
  16. Module 8: Rational Numbers Part 5 Quotients of Decimal Fractions
  17. Module 8: Solutions Exercise Set 8 Form B
  18. Module 8 Supplement: The Calculator (The Good and the Bad)
  19. Module 9: Introduction to Constant Rates
  20. Module 9: Solutions Exercise Set 9 Form B
  21. Module 10: Application of Constant Rates to Measurement
  22. Module 10: Solutions Exercise Set 10 Form B
  23. Module 11: Selected Topics in Non-Constant Rates
  24. Module 11: Solutions Exercise Set 11 Form B
  25. Module 11: Appendix: More on Rectilinear Figures
  26. Module 12: Arithmetic as the Gateway to Algebra
  27. Module 12: Solutions Exercise Set 12 Form B
  28. Module 12: Appendix: Using Formulas

2. Gateways to Mathematics Textbook

Even with new technology, there are people who learn best by reading. If this is the case, you can read the textbook which is available on our site in pdf format. Written material is presented in the form of a series of connected Illustrative Examples. The solution of each example, along with enrichment commentary, accompanies each example.

Gateways to Mathematics Textbook (with illustrations and solutions)

3. GTM Study Guide

The GTM Study Guide gives you a chance to see if you have internalized what you have seen and / or read.

GTM Study Guide

4. PowerPoint Presentations

The final component of our arithmetic course is a series of slide shows developed by Herb Gross and Rick Medeiros that can be used as an alternative or supplement to the text and videos. By adding animation to mathematical concepts, they add a unique dimension to learning.

PowerPoint Presentations

The videotaped lectures were produced in 1985. Since that time, Herb has refined the material in the videos; these changes are reflected in the Powerpoint presentations. Our approach to learning arithmetic, while very logical and user friendly, is not a "quick fix". If you have the patience and commitment to learn arithmetic in a meaningful way that will be easy for you to internalize then this is the course for you! You are now prepared to start the course so... study hard and have fun!

Calculus Revisited (MIT OCW)

Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

MIT OpenCourseWare Class Pages YouTube Videos*

*For those of you who are using only the video lectures, the links above on the right will take you to the video playlists that MIT has made available on YouTube.

Algebra by Example (Text + Solutions)

The format of the text is very similar to the format of our "Gateways to Mathematics" arithmetic text. Each chapter begins with one or two introductory expository paragraphs followed by an Illustrative Example that applies the exposition to solving a specific problem followed by a solution with commentary. At the end of each section in the chapter there are exercises and at the end of each chapter there is a more extensive set of exercises. The solution manual contains the solution plus additional commentary for many of the exercises.

View the text and Study Guide

The Game of Algebra 40 Lessons

The “Game of Algebra” video course evolved in 1993 when the “Algebra by Example” and the Student Solution text went out of print. We had received reviews that indicated that users liked both the content and the format of the texts; and for that reason we wanted to find a way to preserve this valuable resource. Through the North Carolina Department of Community Colleges and Cape Fear Community College in Wilmington NC, we received a Perkins Grant to develop a series of 40 video lectures in basic algebra. Once the videos were recorded, we developed the accompanying written material.

Part 1 of the course is divided into 24 lessons and each lesson is accompanied by four Powerpoint presentations.

Part 2 of the course is divided into lessons 25 - 40; the accompanying Powerpoints are not yet available. The material covered in Part 2 is usually found in the second course in Algebra.

Because different students will likely use different textbooks, the algebra videos are not linked to any one textbook but do match the slide show presentations. There is a suggested mapping from video to text sections in the text section.

  1. Lecture 1: Preface to Gateways to Algebra
  2. Lecture 2: Introduction to Gateways to Algebra, Part 1
  3. Lecture 3: Introduction to Gateways to Algebra, Part 2
  4. Lecture 4: Introduction to Signed Numbers
  5. Lecture 5: Subtracting Signed Numbers
  6. Lecture 6: Multiplying and Dividing /signed Numbers
  7. Lecture 7: Motivation for Using Exponents
  8. Lecture 8: The Arithmetic of Whole Number Exponents
  9. Lecture 9: Scientific Notation And Significant Figures
  10. Lecture 10: The Game Of Mathematics, Part I
  11. Lecture 11: The Game Of Mathematics, Part 2
  12. Lecture 12: Application to Algebra
  13. Lecture 13: Linear Relationships
  14. Lecture 14: Review of Linear Relationships
  15. Lecture 15: Two Enrichment Examples of Linear Relationships
  16. Lecture 16: Solving mx + b = nx + c, Part 1
  17. Lecture 17: Solving mx + b = nx + c, Part 2
  18. Lecture 18: Introduction to Sets, Functions and Graphs
  19. Lecture 19: Some Special Functions
  20. Lecture 20: Introduction to Exponential Functions
  21. Lecture 21: Introduction to Inverse Functions
  22. Lecture 22: Introduction to Systems of Linear Equations
  23. Lecture 22: More on Systems of Linear Equations
  24. Lecture 23: Word Problems, Non-Algebraic Solutions
  25. Lecture 24: Word Problems, Algebraic Solutions
  26. Lecture 25: Introduction to Polynomials
  27. Lecture 26: Addition and Subtraction of Polynomials
  28. Lecture 27: Multiplication of Polynomials
  29. Lecture 28: Special Products of Polynomials
  30. Lecture 29: Factoring
  31. Lecture 30: Division Of Polynomials
  32. Lecture 31: Introduction to Quadratic Equations
  33. Lesson 32: Solving Quadratic Equations By Completing The Square
  34. Lesson 33: The Quadratic Formula
  35. Lesson 34: The Pythagorean Theorem
  36. Lesson 35: Graphical Solutions
  37. Lesson 36: Graphing Quadratics
  38. Lesson 37: Extending The Number System
  39. Lesson 38: Angles as A Measure of Direction
  40. Lesson 39: Introducing the Square Root of -1
  41. Lesson 40: Application of Non Real numbers to Quadratic equations

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