Mathematics 2010-2: Introduction to Proofs

Class Information:

• Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)
• e-mail tag: jdhsmith at the university address. Avoid Canvas messaging!
• Office Hours: Mon. 8:50 - 9:40 am; Wed. 8:50 - 9:40 am; Fri. 8:50 - 9:40 am, 2:15 - 3:05 pm (subject to change).
• Academic grade points: 80% for in-class assignments and homework (last due Monday 5/4); 20% for the final (Wed. 5/13, 7:30 am). Additional points for attendance at random times.
• Important notes: Accessibility statement   Free expression statement
  Class absence memo   AI policy

Textbooks:

• (BP)  R. Hammack, Book of Proof, 3rd. ed. ISBN 978-0-9894721-2-8.
• (BA)  J. Lebl, Basic Analysis: Introduction to Real Analysis, Volume I.

Study Plan:

• Regular attendance, fulfillment of homework assignments (with the techniques of the class}, and active participation in class are the prerequisites for success. Except in extreme circumstances, no accommodation can be given for failure to meet these responsibilities.
• The definitive version of the material will be presented in class; it is often not the version in the textbooks.
• Taking notes in class and building a personal concept list are strongly recommended. Passive lecture attendance and video-watching are not generally helpful.

Prime Learning Objective: To understand that "If you are unsure about the correctness of a solution, then you do not yet have a solution." [Lebl, https://www.jirka.org/ra/]

Syllabus: Sets, logic, proofs in algebra and calculus.

Assignments

Note: In these assignments, (BP) and (BA) refer to the versions of the textbooks from the links above. The day-to-day assignments, referring to reading sections and exercises from the textbooks, are for completion singly or in self-organized groups between successive classes, ready for active discussion in class on the target date. Each assigned problem should be attempted.

• Click here for the First Graded Homework in Portable Document Format (due 2/25).
• 2/20 for 2/23: Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16.
  Lesson summary
• 2/18 for 2/20: Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26.
  Lesson summary
• 2/16 for 2/18: Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12.
  Lesson summary
• 2/11 for 2/13: Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8.
  Lesson summary
• 2/9 for 2/11: Read (BP) Sections 2.7 to 2.9; do (BP) Exercises 2.7: 4, 8, 10; 2.9: 2, 4, 6, 10.
  Lesson summary
• 2/6 for 2/9: Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10; 2.6: 6, 8, 12, 14.
  Lesson summary
• 2/4 for 2/6: Read (BP) Sections 2.3, 2.4; do (BP) Exercises 2.3: 2, 4, 8, 10; 2.4: 2, 4.
  Lesson summary
• 2/2 for 2/4: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10.
  Lesson summary
• 1/28 for 1/30: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 4, 6, 9, 14.
  Lesson summary
• 1/26 for 1/28: Read (BP) Sections 1.3 to 1.7; do (BP) Exercises 1.3: 2, 4, 10; 1.4: 4, 5; 1.5: 2(a)-(c), 4(f)(g)(h); 1.6: 2(a),(f),(g); 1.7: 10, 12.
  Lesson summary
• 1/22 for 1/26: Read (BP) Section 1.2; do (BP) Exercises 1.2: 2, 4, 8, 12, 20.
  Lesson summary
• 1/21 for 1/23: Read (BP) Section 1.1; do (BP) Exercises 1.1: 1-4, 17-20 (write in mixed notation!), 30-33, 40, 42, 44.
  Lesson summary

Link to syllabi of previous semesters.