The grading system is designed to be standards-based, i.e. your grade should reflect your current understanding, not an average of all attempts.  That means you can throw away old grades and replace them with new ones.  However, I cannot test everything on the last day, so over the course of semester you will demonstrate mastery of all the topics.  An even pace is key to success.

You will have several opportunities to demonstrate mastery on the following badges.  Grades will be 0, 0.5 or 1, representing no, partial and full mastery.  There will be several attempts, and your grade can only go up with new attempts.  Attaining a ‘0.5’ or ‘1’ means you have partially or fully earned the badge.  Your grade will depend on how many badges you have earned.

• Sets I: basic definitions including set, element, equality, empty, cardinality, subset
• Sets II:  operations (union, intersection, difference), universe, complement, Venn diagram
• Sets III:  Set-builder notation, interval notation
• Sets IV: ordered pairs, Cartesian products and powers, subset and powersets, including cardinality of such
• Counting I: basic (subsets, independent choices)
• Counting II: advanced (possible overcounting)
• Logic I:  boolean expressions and truth tables
• Logic II:  converse and contrapositive
• Logic III:  quantifiers (for all, there exists)
• Logic IV:  negating statements
• Logic V:  logical equivalence, logical laws and algebraic manipulations of boolean expressions
• Relations I: basic definitions, ordered pairs and arrow diagrams
• Relations II: properties of relations (transitive, symmetric, reflexive, equivalence)
• Modular Arithmetic (computation, inverse by verification)
• Functions I:  definitions (domain, codomain, range, image and preimage)
• Functions II:  definitions (injective, surjective and bijective)
• Function III:  composition of functions, identity function, and inverse functions
• Proofs I:  setting up a proof by contradiction
• Proofs II:  setting up a proof by contrapositive
• Proofs III:  setting up an inductive proof

There are 20 badges.  Each one has an attainment score of 0, 0.5 or 1.  Your grade will be (sum of scores) / 20.

##### Info on Oral Badge exams

To do an oral exam, you must come prepared with a study sheet you have created.  It should be a full page (seriously), with your best synthesis of the relevant material.  It should include:

• any relevant definitions
• any relevant facts/theorems
• explanations of notation
• important notes and clarifications
• and especially, examples you have created yourself, chosen to illustrate important pitfalls and clarify important points that may have tripped you up on the written quizzes
• DO NOT just copy notes from textbook, zoom lectures, etc.  You should learn the definitions, understand them, and then generate them from your brain.  Don’t copy.  Copying doesn’t help you learn.  The examples should be of your own creation, not from the book or notes.

In the oral exam, we will go over your study sheet (be prepared to share it somehow), and I will make any necessary corrections.  Then, if I’m sufficiently impressed with the study sheet, I’ll have you work some problems for me on the spot to earn your badge.

Set up the exam ahead of time or just show up at office hours.

## 35% Proof

Click here for my grading rubric.  You will be quizzed frequently (approximately once weekly), and 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 (i.e. you will get zero), or only receive partial credit.

Your score will be made up of the best half of your quizzes (strictly speaking, the best $\lceil n/2 \rceil$ of n total quizzes).  Missed quizzes are zero, and there are no makeup quizzes.

### 10% Participation and Diligence

I ask for participation because it is the medium by which the course is taught.  You learn by doing.

I will observe whether you are coming prepared to class (having done the Daily Post tasks), and participating helpfully in class will count toward this grade.  I will periodically check daily homework for completeness.  I will observe whether you are demonstrating leadership and helpfulness in a group (this can come in many forms, including asking useful questions, explaining your thoughts, keeping the group on task, etc.)  I reserve the right to base this grade on available evidence as I see fit, according to this rubric:

10/10 — attends regularly (at most 6 times absent), always (or very nearly always) participates helpfully in groupwork, does daily post tasks regularly (at least 36 of the 45 days).

6/10 — attends most of the time, more than half the time is spent working during groupwork time, does daily post tasks half the time

2/10 — has attended class sometimes, has done groupwork sometimes, has done daily post tasks sometimes, throughout the semester.

I can give intermediate grades by interpolating this rubric.