Mathematics 2010-1: 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. 9:55 - 10:45 am; Wed. 9:55 - 10:45 am, 2:15 - 3:05 pm; Fri. 9:55 - 10:45 am (subject to change).
• Academic grade points: 80% for in-class assignments and homework; 20% for the final homework (due Wed., 12/9). Additional points for attendance at random times.

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, working the assigned practice problems (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, primary version of the material will be presented in class. The textbooks offer alternative, secondary versions for comparison, and host the practice problems.
• 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 practice problem 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.

• 10/14 for 10/16: Read (BP) Chapter 10 through Prop. 10.1; do (BP) Exercises 10: 2, 4, 6, 8, 16, using induction or otherwise.
  Lesson summary
• 10/12 for 10/14: Read (BP) Section 3.6; do (BP) Exercises 3.6: 2, 4, 8, 10, 12.
  Lesson summary
• Click here for the First Practice Test in Portable Document Format
• 10/5 for 10/7: Read (BP) Chapter 9 [but avoid disconnected inequalities like those in Examples 9.3 and 9.5]; do (BP) Exercises 9: 4, 12, 16, 28, 30, 34.
  Lesson summary
• 10/2 for 10/5: Read (BP) Sections 8.1 to 8.3; do (BP) Exercises 8: 4, 6, 8, 20, 22.
  Lesson summary
• 9/30 for 10/2: Read (BP) Section 7.1 (omitting final proposition) and Section 7.3 up to WARNING; do (BP) Exercises 7: 2, 4, 12, 18, 20.
  Lesson summary
• Click here for the First Graded Homework in Portable Document Format (due to hand in on paper, end of class on 9/30).
• 9/28 for 9/30: Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10.
  Lesson summary
• 9/25 for 9/28: Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16.
  Lesson summary
• 9/23 for 9/25: Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26.
  Lesson summary
• 9/21 for 9/23: Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12.
  Lesson summary
• 9/16 for 9/18: Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8.
  Lesson summary
• 9/14 for 9/16: Read (BP) Sections 2.7 to 2.9; do (BP) Exercises 2.7: 4, 8, 10; 2.9: 2, 4, 6, 10.
  Lesson summary
• 9/11 for 9/14: Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10; 2.6: 6, 8, 12, 14.
  Lesson summary
• 9/9 for 9/11: Read (BP) Sections 2.3, 2.4; do (BP) Exercises 2.3: 2, 4, 8, 10; 2.4: 2, 4.
  Lesson summary
• 9/4 for 9/9: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10.
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• 8/31 for 9/2: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 4, 6, 9, 14.
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• 8/28 for 8/31: 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
• 8/26 for 8/28: Read (BP) Section 1.2; do (BP) Exercises 1.2: 2, 4, 8, 12, 20.
  Lesson summary
• 8/24 for 8/26: 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.