One of the applications of Number Theory is in Modular Arithmetic.

One of the applications of Modular Arithmetic is in the calculation of the Check Digit of an International Standard Book Number (ISBN).

Students will:

(1.) Perform basic arithmetic operations (addition, subtraction, multiplication, and division) on integers.

(2.) Solve applied problems on numbers.

(3.) Discuss the concepts of: Divisibility, Factors, and Multiples.

(4.) Meet one of the learning objectives of the VCCS (Virginia Community College System) standards for:

MTH 111: Basic Technical Mathematics

*
(Provides a foundation in mathematics with emphasis in arithmetic, unit conversion, basic algebra, geometry and trigonometry.).
*

MTH 133: Mathematics for Health Professions

MTH 154: Quantitative Reasoning

(5.) Meet the QM (Quality Matters) and USDOE (United States Department of Education) requirements for distance education as regards the provision of RSI (Regular and Substantive Interaction).

Federal Register: Distance Education and Innovation

St. John's University: New Federal Requirements for Distance Education: Regular and Substantive Interaction (RSI)

Student – Content Interaction: Very high

Student – Student Interaction: Flexible

Student – Faculty Interaction: Flexible

May you please:

(I.) Review the notes provided for you.

(II.) Review the general project requirements.

(III.) Review the example guide.

(IV.) Complete the project.

ISBN stands for **International Standard Book Number.**

It is a **unique identifier** for any **published book.**

It is important for the publication, marketing, tracking, and the library use of books among others.

Published books include printed books, eBooks, and audio books among others.

Most published books such as printed books, eBooks, and audio books have ISBNs.

__ISBN-10__ (modulo 11)

Prior to 2007, books were issued ISBN-10.

This was developed in modulo 11.

This implies that the digits are from 0 through 10 (mod 11)

Only 10 digits are allowed.

*
Student: So, only ten digits are allowed?
Teacher: Yes, that is the reason for ISBN-10
Student: And the digits could be from 0 through 10?
Teacher: Yes, that is correct.
Do you know why?
Student: Because the system is in Modulo 11.
Teacher: Correct...
Student: What if one or more of the digits was 10?
Teacher: Very good question.
So, the ISBN-10 has 10 digits
The first 9 digits could be numbers from 0 - 9
But, the last digit, the 10th digit, which is also the check digit could be any number from 0 - 10
When the check digit is 10, it is written as X
*

The first 9 digits could be numbers from 0 – 9

The last digit is the 10th digit, and it is the check digit.

It could be any number from 0 – 10

When the check digit is 10, it is written as

1st Approach: Multiplication-Modulo Approach

(a.) Multiply each of the 9 digits respectively by each of the digits 0 – 9 in that order (ascending order)

(b.) Determine the sum of the products.

(c.) Determine the sum modulo 11

The check digit is the sum modulo 11

2nd Approach: Multiplication-Modulo-Subtraction Approach

(a.) Multiply each of the 9 digits respectively by each of the digits 10 – 2 in that order (descending order)

(b.) Determine the sum of the products.

(c.) Determine the sum modulo 11. This is the remainder.

(d.) Subtract the remainder from the modulo.

The check digit is the difference between the modulo and the remainder.

From 2007 till date, ISBN-13 is used.

It was developed in modulo 10.

This implies that the numbers are from 0 through 9 (mod 10)

Only 13 digits are allowed.

Approach: Multiplication-Modulo-Subtraction Approach

(a.) Multiply each of the 12 digits respectively by 1 and 3 in a repeating order

(b.) Determine the sum of the products.

(c.) Determine the sum modulo 10. This is the remainder.

(d.) Subtract the remainder from the modulo.

The check digit is the difference between the modulo and the remainder.

The

For ISBN-10, the check digit is the 10th digit.

For ISBN-13, the check digit is the 13th digit.

The Check Digit:

(1.) Determines whether an ISBN is valid or invalid.

If the calculation of the ISBN leaves a remainder of 0, then the ISBN is valid.

If the calculation of the ISBN does not have a remainder of 0, then the ISBN is invalid.

(2.) Verifies if an ISBN was recorded/entered correctly.

If a user enters the all the digits but the check digit of an ISBN into an appropriate system (a system designed for ISBNs); the system calculates the check digit and compares it with the check digit entered by the user.

If the digits match, the ISBN was entered correctly.

If the digits do not match, the ISBN was not entered correctly.

(3.) is used to convert an ISBN-10 to ISBN-13.

(4.) is used to convert an ISBN-13 to ISBN-10.

(I.) Remove the check digit.

This leaves us with 9 digits.

(II.) Append the number: 978 in front of the remaining digits.

This gives 12 digits.

(III.) Calculate the check digit for the 12 digits.

This gives 13 digits...the ISBN-13.

(I.) Remove the check digit.

This leaves us with 12 digits.

(II.) Remove the number: 978 from the front of the remaining digits.

This gives 9 digits.

(III.) Calculate the check digit for the 9 digits.

This gives 10 digits...the ISBN-10.

(1.) This is an individual project.

You may collaborate with one another. However, it is not a group project.

Students may work together. However, each student must submit own project.

No two students should use the same published book.

(2.) Find your favorite **good** published book or any good published book.

Also, please avoid controversial/opinionated/subjective books such as history books and the like.

Preferably, find a mathematics textbook/eText. This is because mathematics textbooks are
*typically* not controversial.

The published book must have:

(a.) ISBN-10

(b.) ISBN-13

(3.) The image of the part of the book that shows the ISBN-10 and the ISBN-13 must be included.

Please use the **Insert** → **Pictures** icon to insert the image directly.

The image should be very clear.

(4.) As a student, you have free access to Microsoft Office suite of apps.

(a.) Please download the **desktop apps of Microsoft Office** on your desktop/laptop (Windows and/or Mac only).

Do not use a chromebook.

Do not use a tablet/iPad.

Do not use a smartphone.

Do not use the web app/sharepoint access of Microsoft Office.

(*Please contact the IT/Tech Support for assistance if you do not know how to download the desktop app.*)

In that regard, the project is to be typed using the desktop version/app of Microsoft Office Word **only.**

(b.) The file name for the Microsoft Office Word project should be saved as: **firstName**–**lastName**–**project**

Use only hyphens between your first name and your last name; and between your last name and the word, project.

No spaces.

(c.) For all English terms/work: use Times New Roman; font size of 14; line spacing of 1.5.

Further, please make sure you have appropriate spacing between each heading and/or section as applicable.

Your work should be well-formatted and visually appealing.

(d.) For all Math terms/work: symbols, variables, numbers, formulas, expressions, equations and fractions among others,
the Math Equation Editor is required.

(i.) The font is set to Cambria Math by default (set it to that font if it is not); font size of 14, and
align accordingly (preferably left-aligned).

(ii.) To ensure appropriate spacing between your Math work, use a line spacing of 2.0.

Alternatively, you may use line spacing of 1.5 but insert a space after each equation as applicable.

Your work should be well-formatted, organized, well-spaced (not compact), and visually appealing.

(e.) Include page numbers. You may include at the top of the pages or at the bottom of the pages but not both.

(5.) All work must be shown.

If you use any variables, please define your variables accordingly.

Please ensure your answers matches the ISBN-10 and ISBN-13 on the book you used.

(6.) Please review the examples I did.

You may __not__ do the same examples that I did.

These are the minimum expectations.

(7.) Mr. C (SamDom For Peace) wants you to do this real-world project very well.

Hence, he highly recommends that you submit a draft so he can give you feedback.

(a.) __First__: (**Required**): Please submit a clear image of the section of the book/resource
that shows the ISBN-10 and ISBN-13 in the * Projects: ISBNs* page in the Canvas course.

The clear image should clearly show the ISBN-10 and ISBN-13 in the book.

I shall review and respond.

(b.)

Draft projects are not graded because they are drafts. They are only for feedback.

If your professor gives you an opportunity to submit a draft, please use that opportunity.

Submitting drafts is highly recommended. Submitting drafts is not required.

It is highly recommended because I want to give you the opportunity to do your project very well and make an excellent grade in it.

Please turn in your draft in the

You may also send it to me via email (if you do not want your colleagues to see my comments and learn from the comments).

I shall review and provide feedback.

Then, review my feedback and make changes as necessary.

Keep working with me until I give you the

When everything is fine (after you make changes as applicable based on my feedback), please submit your work in the appropriate area:

Only the projects submitted in the appropriate place in the Canvas course are graded.

(8.) All work must be turned in by the final due date to receive credit.

Please note the due dates listed in the course syllabus for the submission of the draft and the actual project. In the course syllabus, we have the:

(a.) Initial due date for the Project Draft: Please turn in your draft.

(b.) Initial due date for the Project: If your draft is not ready for submission, keep working with me. Make changes based on my feedback and keep working with me.

If you prefer not to turn in a draft, please review all the resources provided for you and do your project well and submit.

(c.) Final due date for the Project Draft: This is necessary if you want a written feedback for your draft.

After this date, written feedback would not be provided for your draft. However, verbal feedback would still be provided during Office Hours/Student Engagement Hours/Live Sessions.

(d.) Final due date for the Project: All work must be turned in by this date to receive credit.

After this date, no work may be accepted.

The use of a table is optional.

These minimum information including the calculations are required.

Name: | Your name |

Date: | The date |

Instructor: | Samuel Chukwuemeka |

Project: | Number Theory Application: Check Digits for International Standard Book Numbers (ISBNs) |

Book Title: Digital Access Title: |
Finite Mathematics for the Managerial, Life, and Social Sciences. WebAssign for Finite Mathematics for the Managerial 5 Months |

Copyright Year, Edition, and ISBNs: |
© 2018 12th edition ISBN-10: 133787972X ISBN-13: 9781337879729 |

Objectives: |
(1.) Verify the check digit for ISBN-10 (2.) Verify the check digit for ISBN-13 (3.) Convert ISBN-10 to ISBN-13 (4.) Convert ISBN-13 to ISBN-10 |

Calculations: |
Please see the calculations below.
Use any approach you prefer. Write the name of any approach you use. |

References: |
Cite your source(s) accordingly.
Indicate the type of citation format. |

1st Approach: Multiplication-Modulo Approach

$ 1 * 1 = 1 \\[3ex] 3 * 2 = 6 \\[3ex] 3 * 3 = 9 \\[3ex] 7 * 4 = 28 \\[3ex] 8 * 5 = 40 \\[3ex] 7 * 6 = 42 \\[3ex] 9 * 7 = 63 \\[3ex] 7 * 8 = 56 \\[3ex] 2 * 9 = 18 \\[3ex] \Sigma Products = 263 \\[3ex] Remainder = 263 \mod 11 = 10 \\[3ex] Check\;\;digit = Remainder = 10 = X \\[5ex] $ 2nd Approach: Multiplication-Modulo-Subtraction Approach

$ 1 * 10 = 10 \\[3ex] 3 * 9 = 27 \\[3ex] 3 * 8 = 24 \\[3ex] 7 * 7 = 49 \\[3ex] 8 * 6 = 48 \\[3ex] 7 * 5 = 35 \\[3ex] 9 * 4 = 36 \\[3ex] 7 * 3 = 21 \\[3ex] 2 * 2 = 4 \\[3ex] \Sigma Products = 254 \\[3ex] Remainder = 254 \mod 11 = 1 \\[3ex] Check\;\;digit = Modulo - Remainder \\[3ex] = 11 - 1 \\[3ex] = 10 \\[3ex] = X \\[5ex] $

Approach: Multiplication-Modulo-Subtraction Approach

$ 9 * 1 = 9 \\[3ex] 7 * 3 = 21 \\[3ex] 8 * 1 = 8 \\[3ex] 1 * 3 = 3 \\[3ex] 3 * 1 = 3 \\[3ex] 3 * 3 = 9 \\[3ex] 7 * 1 = 7 \\[3ex] 8 * 3 = 24 \\[3ex] 7 * 1 = 7 \\[3ex] 9 * 3 = 27 \\[3ex] 7 * 1 = 7 \\[3ex] 2 * 3 = 6 \\[3ex] \Sigma Products = 131 \\[3ex] Remainder = 131 \mod 10 = 1 \\[3ex] Check\;\;digit = Modulo - Remainder \\[3ex] = 10 - 1 \\[3ex] = 9 \\[3ex] $

(1.) Remove the check digit, X: we have 133787972

(2.) Replace it with the check digit for ISBN-13: we have 1337879729

(3.) Append 978 in front of the remaining digits: we have 9781337879729

∴ ISBN-13 is 9781337879729

OR

(1.) Remove the check digit, X: we have 133787972

(2.) Append 978 in front of the remaining digits: we have 978133787972

(3.) Calculate the check digit: we already calculated it to be 9

∴ ISBN-13 is 9781337879729

(1.) Remove the check digit, 9: we have 978133787972

(2.) Replace it with the check digit for ISBN-10: we have 978133787972X

(3.) Remove the number: 978 from the front of the remaining digits: we have 133787972X

∴ ISBN-10 is 133787972X

OR

(1.) Remove the check digit, 9: we have 978133787972

(2.) Remove the number: 978 from the front of the remaining digits: we have 133787972

(3.) Calculate the check digit: we already calculated it to be X

∴ ISBN-10 is 133787972X

Second Sample:

Third Sample:

Let students know you are willing to help.

Chukwuemeka, Samuel Dominic (2023). *Mathematics Education Courses.*
Retrieved from https://mathematicseducation.appspot.com/

*Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach*, 12th
Edition - 9781337405782 - Cengage. (n.d.). www.cengage.com.
Retrieved October 12, 2023, from
https://www.cengage.com/c/finite-mathematics-for-the-managerial-life-and-social-sciences-12e-tan/9781337405782/

ISBN Information. (n.d). Retrieved from
https://isbn-information.com/check-digit-for-the-13-digit-isbn.html