What, when, where?
| Course ID: | Math 571 |
| Time: | TuTh 9:30—10:45AM |
| Place: | Sterling Hall 1313 |
Instructor
| Mariya Soskova | |
| Office: | 523 Van Vleck |
| Email: | msoskova@math.wisc.edu |
| Steffen Lempp | |
| Office: | 525 Van Vleck |
| Email: | lempp@math.wisc.edu |
| Office hours: | TR 8:30 - 9:20 and 11:00PM—11:50 AM |
Course description and textbook
| This course provides an introduction into mathematical logic, including the syntax and semantics of first-order languages, a formal calculus for proofs, Gödel's completeness theorem and the compactness theorem, nonstandard models of arithmetic, decidability and undecidability, and Gödel's incompleteness theorem. We will mainly be following A Mathematical Introduction to Logic, Second Edition by Herbert B. Enderton, ISBN 978-0122384523. Homework will include problems form this book. Link to canvas page |  |
Exams and evaluation
| Midterm 1: | October 17th. For practice you can find Midterm 1 from Fall 2017 here. The solutions can be found here. |
| Midterm 2: | November 14th. For practice you can find Midterm 2 from Fall 2017 here. The solutions can be found here. |
| Final: | December 17th (12:25PM—2:25PM) Sterling 1313. For practice you can find the Final from Fall 2017 here. The solutions can be found here. |
Homework
Every Friday you will receive a new homework assignment. Homework will be due the following Thursday at the beginning of class. Late homework will not be accepted unless in case of emergency.
Homework will be graded for completeness and one problem (selected at random) will be graded for correctness.
Recall that this is a proof-based course, and thus a strict level of rigor is necessary in your solutions. Pictures are never proofs, but are always encouraged along with proofs. Your solution should not be just a sequence of equations and formulas, write in complete sentences.
It is okay, even encouraged, if you work on the homeworks in groups. If you do, please acknowledge that in your homework. The solutions you submit, have to be written by each student individually. Copying is not allowed and will be acted against.
To help make grading more streamlined, please do the following:
- Tear off all spirals from your paper.
- Staple your your homework together.
- Write and highlight your name on the front of the packet.
| HW 1(due Sept 12) | Section 1.1: Ex 1, Ex 3, Ex 5. |
| HW 2(due Sept 19 ) | Section 1.2: Ex 2, Ex 5, Ex 8, Ex 9, Ex 10 a and b. |
| HW 3(due Sept 26 ) | Section 1.2: Ex 11, Ex 12; Section 1.4: Ex 1(Omit the question about C4), EX 2; As well as the exercise you can find here. |
| HW 4(due Oct 3) | Section 1.5: Ex 3 (The connective # is defined on page 45. Hint: Show that a Boolean function G realized with the given connectives has the property that G(T,T,...,T) is never equal to G(F,F,...,F), Ex 4, Ex 9, Ex 10; Ex 11. |
| HW 5(due Oct 10) | Section 1.7: Ex 1, Ex 4, Ex 5, as well as the exercises you can find here. |
| HW 6(due Oct 17) | Section 1.7 10, 12, Section 2.1: Ex 3, Ex 4, Ex 5; |
| HW 7(due Oct 31) | Section 2.2: Ex 1, Ex 2, Ex 4, Ex 8, Ex 9, Ex 11; |
| HW 8(due Nov 7) | Section 2.2: Ex 5, Ex 6, Ex 12 a, b, Ex 15, Ex 16, Ex 26, Ex 27 |
| HW 9(due Nov 14) | Section 2.4: Ex 2, Ex 4 (a proof that a deduction exists suffices), Ex 9, Ex 11. |
| HW 10(due Dec 3) | Section 2.5: Ex 2, Ex 6, Ex 8, Section 2.6: Ex 2, Ex 7., Ex 8, Ex 9 |
| HW 11(due Dec 10) | Section 3.3: Ex 1, Ex 2, Ex 3, Ex 5, Ex 7, Ex 10. |
Honors Assignment
To complete this class with honors, you must turn in several Honors Assignments that will be posted in the course of the semester. Each assignment is worth 10 points and is counted towards the homework grade. | HA 1(due Oct 10) | You can find the first assignment here . For Problem 1 you can use the fact that the sum of the entries in the nth row of Pascal's triangle is the nth power of 2. (See here) |
| HA 2(due Nov 12) | You can find the second assignment here . |
| HA 3(due Dec 10) | Research Section 2.8 in the textbook and complete Ex 1, Ex 2, Ex 3, Ex 4, and Ex 5. |