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).
• Finals Week Office Hour: Mon. 1:30 - 3 pm.
• 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 Practice Final in Portable Document Format.
• 5/6 for 5/8: Read (BA) Section 2.5.3.
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• 5/4 for 5/6: Read (BA) Section 2.5.5.
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• Click here for the Third Graded Homework in Portable Document Format (due to hand in on paper, end of class on 5/4).
• 5/1 for 5/4: Read (BA) Sections 2.5.1-2; do (BA) Exercises 2.5.7: 1, 2, 3(d).
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• 4/29 for 5/1: Read (BA) Section 2.4; do (BA) Exercises 2.4.1: 1, 4, 5.
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• 4/27 for 4/29: Read (BA) Sections 3.2.1-3; do (BA) Exercises 3.2.4: 1, 3, 5 (just prove continuity at x = 0).
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• Click here for the Second Practice Test in Portable Document Format
• 4/20 for 4/22: Read (BA) Section 2.2.1 and Prop. 2.2.5; do (BA) Exercises 2.2.5: 1, 2, 3, 5, 7.
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• 4/17 for 4/20: Complete reading of (BA) Section 2.1; do (BA) Exercises 2.1.4: 3, 4, 14, 15, 22.
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• 4/15 for 4/17: Read (BA) Section 2.1 through Section 2.1.1; do (BA) Exercises 2.1.4: 1, 2, 9, 10.
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• 4/13 for 4/15: Read (BA) Section 1.3; do (BA) Exercises 1.3.1: 1, 2, 3, 7.
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• 4/10 for 4/13: Read (BA) Section 1.2.2; do (BA) Exercises 1.2.5: 1, 2, 8.
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• Click here for the Second Graded Homework in Portable Document Format (due to hand in on paper, end of class on 4/10).
• 4/8 for 4/10: Read (BA) Sections 1.2.1 (not proof of Ex. 1.2.3), 1.2.3, 1.2.4; do (BA) Exercises 1.2.5: 4, 7, 9.
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• 4/6 for 4/8: Read (BA) Section 1.1 to just before Definition 1.1.5; do (BA) Exercises 1.1.1: 2, 4, 6, 9.
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• 4/3 for 4/6: Read (BP) Section 14.3.
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• 4/1 for 4/3: Read (BP) Sections 14.1, 14.2; do (BP) Exercises 14.2: 2, 4, 6, 8.
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• 3/30 for 4/1: Read (BP) Sections 12.5, 14.1 (through Theorem 14.1); do (BP) Exercises 12.2: 9, 10; 12.5: 2, 6; 14.1: 4, 6, 8.
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• 3/25 for 3/27: Read (BP) Sections 12.2, 12.4, 12.6; do (BP) Exercises 12.2: 2, 4; 12.4: 2, 6; 12.6: 2, 6.
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• 3/23 for 3/25: Read (BP) Sections 11.1, 11.6, 12.1; do (BP) Exercises 11.1: 2, 4, 12, 14; 12.1: 2, 4, 7, 8, 10.
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• 3/13 for 3/23: Read (BP) Section 10.1; do (BP) Exercises 10: 10, 18, 24, 34, using induction or otherwise.
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• 3/11 for 3/13: Read (BP) Chapter 10 through Prop. 10.1; do (BP) Exercises 10: 2, 4, 6, 8, 16, using induction or otherwise.
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• 3/9 for 3/11: Read (BP) Section 3.6; do (BP) Exercises 3.6: 2, 4, 8, 10, 12.
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• Click here for the First Practice Test in Portable Document Format
• 3/2 for 3/4: 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.
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• 2/27 for 3/2: Read (BP) Sections 8.1 to 8.3; do (BP) Exercises 8: 4, 6, 8, 20, 22.
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• 2/25 for 2/27: 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 2/25).
• 2/23 for 2/25: Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10.
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• 2/20 for 2/23: Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16.
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• 2/18 for 2/20: Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26.
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• 2/16 for 2/18: Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12.
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• 2/11 for 2/13: Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8.
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• 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.
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• 2/6 for 2/9: Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10; 2.6: 6, 8, 12, 14.
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• 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.
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• 2/2 for 2/4: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10.
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• 1/28 for 1/30: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 4, 6, 9, 14.
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• 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.
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• 1/22 for 1/26: Read (BP) Section 1.2; do (BP) Exercises 1.2: 2, 4, 8, 12, 20.
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• 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.
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Link to syllabi of previous semesters.