# Overview

- 30 % content (6 in-class quizzes @ 5% each, opportunity for oral exam makeup)
- 32 % proof-writing (best 4 of 7 in-class quizzes)
- 18 % daily homework (self-evaluated diligence not correctness; allot 60 minutes between
*every lecture*) - 20 % traditional final exam

# Schedule of in-class tests:

- Feb 1
**Proof** - Feb 8
**Counting (see topics below)** - Feb 15
**Proof** - Feb 22
**Proof** - Mar 1
**Set Theory (see topics below)** - Mar 8
**Proof** - Mar 15
**Logic (see topics below)** - Mar 22
**Proof** - Mar 29 SPRING BREAK
- Apr 5
**Relations and Modular Arithmetic (see topics below)** - Apr 12
**Proof** - Apr 19
**Mechanics of Proof (see topics below)** - Apr 26
**Proof** - May 3
**Functions (see topics below)** -
## Final Exam:

*Monday, May 8, 4:30–7 p.m.*

# 30% Content Modules (6 tests @ 5% each)

Each of the following six content modules will have their own in-class quiz (20 minutes).

**Missed Quiz Policy:** If you miss a quiz, you will make it up as an oral exam (see Grade Improvement below).

**Grading:** They will be graded as follows:

- 4: clear understanding, ability to handle novel situations, with the occasional very small error
- 3: basic understanding, consistently correct on standard cases, and some ability to handle novel situations, but some errors
- 2: some evidence of skills/knowledge, especially on the most standard cases, but inconsistent performance
- 1: inconsistent evidence of skills/knowledge
- 0: little or no demonstration of skills or knowledge

**Grade Improvement: **I know that life can interfere with studying, and that in-class tests can fail to reflect your understanding. For this reason, if you are not happy with your in-class performance on any of these tests, you may meet with me for an oral evaluation to raise your grade. First, you will prepare your study sheet and have me or the TA evaluate it via email/discord, making improvements as necessary, and once it is excellent, I will give you an oral examination. ** The deadline to schedule your oral examination is two weeks after the quiz. ** Unfortunately, the final quiz cannot be improved (since no time remains in semester).

##### Set Theory

- basic definitions including set, element, equality, empty, cardinality, subset
- operations (union, intersection, difference), universe, complement, Venn diagrams to visualize these
- Set-builder notation and interval notation
- ordered pairs, Cartesian products and powers, subset and powersets, including cardinality of such

##### Counting

- subsets (addition principle)
- independent choices (multiplication principle)
- possible overcounting (subtraction/division principles)

##### Logic

- boolean expressions and truth tables
- converse and contrapositive
- quantifiers (for all, there exists)
- negating statements
- logical equivalence, logical laws and algebraic manipulations of boolean expressions

##### Relations and Modular Arithmetic

- basic definitions, ordered pairs and arrow diagrams
- properties of relations (transitive, symmetric, reflexive, equivalence)
- modular arithmetic: computation, inverse by verification, possibly more

##### Functions

- domain, codomain, range, image and preimage
- injective, surjective and bijective
- composition of functions
- identity function and inverse functions

##### Mechanics of Proof

- setting up a proof by contradiction
- setting up a proof by contrapositive
- setting up an inductive proof

## 32% Proof (best 4 of 7, 8% each)

Each proof quiz will be taken in class (20 minutes).

**Grading:** Click here for my grading rubric. You will be assigned two scores (one for reasoning, one for writing). If you are unable to provide a useful sample to evaluate writing (that is, I cannot understand well enough to compare what you *wrote* to what you *meant*), you will not obtain a writing score (meaning you will get zero), or only receive partial credit.

**Missed Quiz Policy:** If you miss a quiz, you will get zero. However, we take only the best 4 of 7 for your final grade, and missed quizzes can be among those dropped.

**18% Daily Posts and Diligence**

You are responsible for assigning yourself this grade, using a worksheet I provide. This grade is about your work ethic in the course, not about mathematical correctness. You must hold yourself accountable for your diligence and the completion of daily homework exercises. To give yourself full credit you will need to:

- set aside and use 60 minutes of homework time between each class for daily homework tasks, and use this time with focus and attention (no watching TV in the background).
- hand in your daily tasks on canvas before each lecture
- put in the effort needed to catch up or seek help on material you have not yet mastered
- check your own homework solutions and seek help where needed
- attend class regularly, participate in the in-class activities, and foster a positive learning atmosphere

Daily tasks can be collaborative, and this grade will be based on daily task effort/completion and attendance and productive participation in groupwork in class, participating in the creation of a collegial atmosphere, etc. You may excuse a moderate number of absences and missed daily tasks without need for justification (life happens). *You will track and assign this grade to yourself using this worksheet. *I reserve the right to alter this grade if it is not assigned truthfully or thoughtfully, based on my evidence of your work.

## 20% Traditional Final Exam

*Monday, May 8, 4:30–7 p.m.*

The final exam will look like the in-class quizzes and be graded similarly, but is traditional in the sense that you only get one chance at the test.