## Math 160A (Fall 2022)

### Summary

Math 160A is first course in logic.
We will be mainly concerned with studying *formal proof systems* and model theory.
We will also touch on some set theory, computability theory and maybe some other topics.
One of the chief goals of the course is to prove (and understand!) Godel's incompleteness theorem.

Note that in previous years there has been a 160AB sequence. This year only 160A is offered, so the material covered will be different to make the course self-contained.

There is no required textbook for this course.
However, as an optional textbook we will use Samuel Buss's draft textbook, available here.
If you use this textbook, Professor Buss would be grateful for any **feedback** (typos, comments, etc.).

### Contacts

The instructor is Freddie Manners (email `fmanners`); my office is AP&M 7343.
The TA is Johnny Li (email `jil164`).

### Class and section

Lectures are held on Mondays, Wednesdays and Fridays, 1200–1250. Lectures will be held in-person in WLH-2111 (Warren Lecture Hall). They will be podcasted, but in-person attendance is strongly encouraged.

Section will take place in-person at the advertized times and places.

The Google calendar below has times and locations for all class events.

### Exams

There will be two in-class midterms, on **Monday October 17** (Week 4) and **Monday November 7** (Week 7).

The final exam is on **Thursday December 8**, at 1130–1430.
It is also in-person (location TBD).

You should ensure at the start of the quarter that you can attend these exams.
In general, alternative modalities, dates or times (in particular, remote exams) will *not* be offered.

### Homework

Midterm weeks will have reduced homework loads, but still some homework.

Please note: while discussing homework problems in groups is permitted (and encouraged), your final written-up solutions **must be written by you, by yourself, in your own words**. If your homework appears to have been copied directly from another student (or another source) that may constitute an academic integrity issue. You also may **not** post homework questions or solicit answers on the internet.

### Grading

Your **combined grade** for the course is calculated as follows.
First, your lowest homework score is dropped. Then, take 30% homework + 30% midterms + 40% final.

The letter grade cut-offs will be at least as generous as the following table (but may be more generous). Separately, exam scores may be curved to adjust for difficulty.

A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
---|---|---|---|---|---|---|---|---|---|

97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |

### Resources

In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.

### Provisional schedule

A very rough provisional course schedule is given below. It can and probably will change.

Week | Mon | Wed | Fri | Topic |
---|---|---|---|---|

0 | L1 | Introduction | ||

1 | L2 | L3 | L4 | Propositional logic. Syntax and semantics. Proofs. |

2 | L5 | L6 | L7 | The deduction theorem. The completeness theorem. and applications. |

3 | L8 | L9 | Review |
Digression on computability. |

4 | MT1 |
L10 | L11 | The halting problem. Intro to predicate logic. |

5 | L12 | L13 | L14 | First-order syntax. First-order semantics and models. |

6 | L15 | L16 | Review |
The completeness theorem and applications. |

7 | MT2 |
L17 | X | Applications of completeness. |

8 | L18 | L19 | L20 | The incomplteness theorem. The ZF and ZFC axioms. |

9 | L21 | X | X | Ordinals and recursion. |

9 | L22 | L23 | Review |
More ordinals. Other topics, if time. |

### Office hours

Regular office hours and locations are listed in the table below. However, please **check the calendar below** for any one-off changes or cancellations.

Instructor / TA | Location | Regular hours |
---|---|---|

Freddie Manners | AP&M 7343 | Mondays 1:30pm – 2:30pm, Wednesdays 10:30am – 11:30am |

Johnny Li | HSS 5086 | Wednesday 3:00pm – 5:00pm |

### Course calendar

A link to add this calendar is available on the course's Canvas page.