Mathematics 2010-2: Introduction to Proofs
Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)
e-mail: jdhsmithATiastateDOTedu (substitute punctuation)
Office Hours: M 9:55 am, 11 am; F 9:55 am, 11 am (subject to change).
Academic grade points: 80% for in-class assignments
and homework (last assignment due 12/9);
20% for the final Mon. 12/16, 12 - 2 pm. Additional points for attendance.
Accessibility statement;
Free expression statement.
Class absence memo.
Textbooks:
Study Plan: Regular attendance and active participation in class are the prerequisites for success. Except in extreme circumstances, no accommodation can be given for failure to meet this responsibility. The definitive version of the material will be presented in class; it may not be the version in the textbooks. Taking notes in class is strongly recommended. In general, neither passive lecture attendance nor video-watching are helpful for this class.
Ungraded homework (reading and problems) is regularly assigned as an integral component of the class. To understand the material and develop the necessary skills, each assigned problem should be attempted, ready for discussion in the first half of the following class.
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.
Click here for the Practice Final in Portable Document Format.
12/9 for 12/11: Read (BA) Section 2.5.3.
Lesson summary
Click here for the Third Graded Homework in Portable Document Format (due 12/9).
12/6 for 12/9: Read (BA) Section 2.5.5.
Lesson summary
12/4 for 12/6: Read (BA) Sections 2.5.1-2; do (BA) Exercises 2.5.7: 1, 2, 3(d).
Lesson summary
12/2 for 12/4: Read (BA) Section 2.4; do (BA) Exercises 2.4.1: 1, 4, 5.
Lesson summary
11/22 for 12/2: Read (BA) Sections 3.2.1-3; do (BA) Exercises 3.2.4: 1, 3, 5 (just prove continuity at x = 0).
Lesson summary
11/20 for 11/22: Read (BA) Section 2.2.1 and Prop. 2.2.5; do (BA) Exercises 2.2.5: 1, 2, 3, 5, 7.
Lesson summary
11/18 for 11/20: Complete reading of (BA) Section 2.1; do (BA) Exercises 2.1.4: 3, 4, 14, 15, 22.
Lesson summary
Click here for Practice Test #2 in Portable Document Format
11/11 for 11/13: Read (BA) Section 2.1 through Section 2.1.1; do (BA) Exercises 2.1.4: 1, 2, 9, 10.
Lesson summary
11/8 for 11/11: Read (BA) Section 1.3; do (BA) Exercises 1.3.1: 1, 2, 3, 7.
Lesson summary
11/6 for 11/8: Read (BA) Section 1.2.2; do (BA) Exercises 1.2.5: 1, 2, 8.
Lesson summary
11/4 for 11/6: 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.
Lesson summary
Click here for the Second Graded Homework in Portable Document Format (due 11/4).
11/1 for 11/4: Read (BA) Section 1.1 to just before Definition 1.1.5; do (BA) Exercises 1.1.1: 2, 4, 6, 9.
Lesson summary
10/30 for 11/1: Read (BP) Section 14.3.
Lesson summary
10/28 for 10/30: Read (BP) Sections 14.1, 14.2; do (BP) Exercises 14.2: 2, 4, 6, 8.
Lesson summary
10/25 for 10/28: 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.
Lesson summary
10/21 for 10/23: Read (BP) Sections 12.2, 12.4, 12.6; do (BP) Exercises 12.2: 2, 4; 12.4: 2, 6; 12.6: 2, 6.
Lesson summary
10/18 for 10/21: 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.
Lesson summary
10/16 for 10/18: Read (BP) Section 10.1; do (BP) Exercises 10: 10, 18, 24, 34, using induction or otherwise.
Lesson summary
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
Click here for Practice Test #1 in Portable Document Format
10/7 for 10/9: Read (BP) Section 3.6; do (BP) Exercises 3.6: 2, 4, 8, 10, 12.
Lesson summary
10/4 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 10/4: 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 9/30).
9/27 for 9/30: Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10.
Lesson summary
9/25 for 9/27: 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.
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9/20 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
9/13 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 9/13: 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
9/6 for 9/9: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10.
Lesson summary
8/30 for 9/4: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 4, 6, 9, 14.
Lesson summary
8/28 for 8/30: 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) Sections 1.1, 1.2; do (BP) Exercises 1.1: 1-4, 17-20 (write in mixed notation!), 30-33, 40, 42, 44; 1.2: 1, 3, 10, 12, 20.
Lesson summary
Link to syllabi of previous semesters.