Math 1365 - Introduction to Mathematical Reasoning

This course will develop the ability to follow and write complete mathematical arguments.

Instructor: Alina Marian, a.marian@neu.edu, office in 557 Lake Hall.

Lectures: Mon, Wed, Thurs 1:35-2:40 pm, Shillman Hall 415.

Office hours: Mon & Wed 5-6 pm.

Textbooks: Proof in Mathematics: An Introduction, by Albert Daoud and James Franklin; Discrete Mathematics, by Norman Biggs.

Exams: There will be one midterm exam, one final exam, and occasional quizzes.

Grades: Homework and quizzes (35 percent), Midterm (25 percent), Final Exam (40 percent).

Homework: There will be weekly problem sets, due Thursday in class.

• Homework 1 (due September 11): Daoud-Franklin, Chapter 1 - 1, 3, 12, 16; Chapter 2 - 3, 10, 23; Chapter 4 - 7, 8, 10, 11.
• Homework 2 (due September 18): Daoud-Franklin, Chapter 3 - 9, 12, 13, 16; Chapter 5 - 3, 4; Chapter 6 - 3, 6, 8, 11, 12c.
• Homework 3 (due September 25): Daoud-Franklin, Chapter 6 - 16, 25, 27; Chapter 7 - 7, 11, 12, 16, 17.
• Homework 4 (due October 2): Daoud-Franklin, Chapter 8 - 1cd, 2, 4, 5, 7, 9, 10.
• Homework 5 (due October 9).
• Homework 6 (due October 16).
• Homework 7 (due October 23).
• Homework 8 (due October 30): Biggs, Section 10.6 - 2, Section 11.1 - 7, Section 11.2 - 4, Section 11.3 - 2, Section 11.4 - 1.
• Homework 9 (due November 6): Biggs, Section 11.5 - 2, 4; Section 11.8 - 2, 3, 4, 5, 6, 13, 14.
• Homework 10 (due November 13): Biggs, Section 12.1 - 3; Section 12.3 - 1, 2, 4, 5, 6. In addition: calculate S(n,3).
• Homework 11 (due November 20): Biggs, Section 12.4 - 1, 2; Section 12.7 - 1, 2, 3, 12, 13, 14; Section 13.1 - 1, 3; Section 13.3 - 1, 3, 4.
• Homework 12 (due December 1): Biggs, Section 13.2 - 3, 4; Section 13.3 - 5; Section 13.6 - 7; Section 26.3 - 1, Section 26.4 - 1. In addition, solve: (I) x = 4 (mod 5) & x = 7 (mod 11); (II) x = 34 (mod 100) & x = -1 (mod 51).