# Ma 299: Mathematical Proofs

A transition course between lower-level mathematics courses and more abstract/theoretical upper-level courses in which mathematical proofs are essential. Required of students before taking 400-level math courses unless waived by passing the Mathematical Proofs placement test. 1 Credit.

### Spring 2021 Course Information

- Instructor: Melissa Gardenghi
- Course Syllabus

#### Course Resources

- Reaching Dr. Gardenghi/Making an Office Appointment
- Assignment Integrity Expectations
- Documentation Page for Assignments
- Proof Analysis Assignments
- Original Proofs Assignments
- Handouts from Class (updated 4/15)
- Midterm Exam Review Proofs with Solutions
- Final Exam Review Proofs with Solutions

## Additional Resources

- https://math.berkeley.edu/~hutching/teach/proofs.pdf
- https://cs.stanford.edu/~jtysu/proofs.pdf
- https://www.cs.sfu.ca/~ggbaker/zju/math/proof.html
- http://web.stanford.edu/class/.../GuidetoProofs.pdf
- http://web.stanford.edu/.../HowToWriteCorrectnessProof.pdf
- https://faculty.math.illinois.edu/~hildebr/213/inductionsampler.pdf
- https://www.cs.cornell.edu/courses/cs312/.../induction/induct-examples.html
- https://www.cs.cornell.edu/courses/cs2800/.../Lectures/induction.pdf

## Ma 299 Placement Test Information

The placement test may be taken online at any time (submissions are to represent your own work without referencing any outside sources and are usually graded during the semester in 2-3 business days and within 1-2 weeks during academic breaks). Once your proofs have been evaluated, you will be notified of your placement (it will be posted on your checksheet in StudentCentral).

You will be presented with a set of statements to be proved. You will be asked to select any two of the three statements and using only the information provided (no additional research is permitted) prove the statements. If you wish to study/practice your "math proof" skills prior to taking the test, you may find *How to Read and Do Proofs* by Daniel Solow (any edition) useful.

You will then be asked to sign your test indicating the following:

These questions were completed without the use of any helps (this is a closed book/notes/person/internet test) and that at no time (present or future) will I share the test questions with any other person.

The following are the instructions provided and include the grading and submission guidelines:

Present all your work on separate paper. At the top of each sheet put your name and BJU ID number. You will be graded on the following three criteria:

- Use of the correct proof technique (direct proof, contradiction, contrapositive, induction, etc.)
- Clarity of your presentation and flow (is the proof easily followed? are reasons given? are steps left out?)
- Correctness of the proof (is the proof valid)

Choose **two** of the problems given below [not shown] to complete. When you are done use **one** of the following methods to submit your responses. You can see your results on your checksheet once they are entered.

- Scan your proofs and upload them to the BJUOnline/Canvas Assignment.
- Take
digital pictures of your proofs and upload them to the BJUOnline/Canvas Assignment.*clear* - Turn your proofs into Dr. Melissa Gardenghi’s credenza (Al 38).