Check Digits for International Standard Book Number (ISBN)

MATH 2132: Understanding Elementary Mathematics I course outline includes topics such as Whole Numbers, Integers, and Number Theory among others.
Some of the learning objectives for these topics are:
(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.
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).
This project is designed to assess your understanding of the real-world applications of some of the course objectives.
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.

Check Digits for ISBNs

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 X

Given: the 9 digits of an ISBN-10
To Calculate: the check digit
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.

ISBN-13 (modulo 10)
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.

Given: the 12 digits of an ISBN-13
To Calculate: the check digit
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.

Check Digit
The Check Digit of an International Standard Book Number (ISBN) is the last digit of that number.

For ISBN-10, the check digit is the 10th digit.
For ISBN-13, the check digit is the 13th digit.

Why is the Check Digit important?
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.

To convert from ISBN-10 to ISBN-13:
(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.

To convert from ISBN-13 to ISBN-10:
(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.

General Project Requirements

(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 WNMU student, you have access to the Microsoft Office suite of apps.
(a.) You can download and install these apps on your laptop/desktop.
(Please contact the IT/Tech Support for assistance if you do not know.)
In that regard, the project is to be typed using Microsoft Word.

(b.) For all English terms (entire project): use Times New Roman; font size of 14; line spacing of at least 1.5


(c.) For all Math terms: symbols, variables, numbers, formulas, expressions, equations and fractions among others, please use the Math Equation Editor.
(i.) Set the font to Cambria Math; font size of 14; and align accordingly.
(ii.) Insert a space after each each equation as applicable. Make a good work that is organized and spacious.





(d.) 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.) Second: (Highly Recommended): When your book is approved, please submit your draft to me via email (my school email) or in the Projects: Drafts page in the Canvas course at least one week prior to the due date.
Please do not submit any draft if the due date is one week or less.
When you submit your draft, I shall review and provide feedback.
When everything is fine (after you make changes as applicable based on my feedback), please submit your work in the appropriate area in the Canvas course.
Only projects submitted in the Canvas course are graded.
Draft projects are not graded. In other words, projects submitted via email and/or in the Projects: Drafts page are not graded because they are drafts. They are only for feedback and should be submitted at least one week prior to the due date.
If it is past one week before the project is due, please do not submit it as a draft to me. Just do it very well according to the requirements and submit it in the appropriate area (Assignments page: Number Theory Project) in the Canvas course.
Submitting drafts is highly recommended. If your professor gives you an opportunity to submit a draft, please use that opportunity.
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.

(8.) All work must be turned in by the final due date to receive credit.
It is highly recommended that you turn in your draft by the first due date. Then, review my feedback and make corrections as necessary before turning in your final submission by the final due date.
I would not wait till the due dates: the sooner you turn it in, the better.

Example Guide (Number Theory Project)

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:	Please cite your sources accordingly. Indicate the citation format.

Calculations:


ISBN-10: 133787972X (modulo 11)
1st Objective:
Given: 133787972-?
To Calculate: the check digit

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] $ ISBN-13: 9781337879729 (modulo 10)
2nd Objective:
Given: 978133787972-?
To Calculate: the check digit
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] $ 3rd Objective:
Given: ISBN-10: 133787972X
To Convert: to ISBN-13

(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

4th Objective:
Given: ISBN-13: 9781337879729
To Convert: to ISBN-10

(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

References

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