Math Foundations of Computing, F23
Is this a good class to take if I’m not considering further coursework in CS?
You’re welcome here, but it’s likely that you’ll get more out of courses in Math/Stats.
Are the warmups also graded using EMRN grading?
No, warmups are just graded Complete/Incomplete.
Where will warmups be posted?
I put them on the course website, but they’re also linked from Canvas.
What do labs look like for a math class?
You’ll see. 😈
Can I watch lectures and do warmups ahead of time?
That’s totally fine as long as they are fresh in your mind for class.
I like coming to office hours.
That’s great! Everyone else should do that too. 😁
What’s a way in which your previous classmates have helped you feel welcome or supported in your learning?
What’s a way in which your previous classmates have made you feel unwelcome or discouraged in your learning?
🥗🥬🥕🍉🥑🍅🍇🥝🥔🍍🍊🍌🍈🥭🍎🍒🍠🍓🍑🥒🍋🍆🌽🫑🍏🍐🥦🌶
After everyone has spoken, go around again with:
🥗🥬🥕🍉🥑🍅🍇🥝🥔🍍🍊🍌🍈🥭🍎🍒🍠🍓🍑🥒🍋🍆🌽🫑🍏🍐🥦🌶
What’s something you are especially good at?
Were you ever not good at it?
How did you get good at it?
Once everyone has spoken, go around again with:
First Row: How many Learning Targets could a student not satisfy and still earn an A-? How many Labs could a student miss and still earn an A-?
Second Row: describe, in terms of Learning Targets, Labs, and Warmups, a scenario in which a student would earn a B+.
Third Row: which of these assignment types have “partial credit”? Which of them have a chance to try again?
Mathematical writing is something we’ll be doing a lot of in this course, and we’re about to start with it in our upcoming warmup and lab assignment. Let’s compare and contrast two examples of mathematical writing.
Prove that the sum of two even integers is also even.
\(2i + 2j = 2(i + j)\)
Proposition 1 (Sum of Even Integers is Even) Let \(m\) and \(n\) be any two even integers. Then, \(m+n\) is also an even integer.
Proof. Let \(m\) and \(n\) be any two even integers. Then, there is some integer \(i\) such that \(m = 2i\), and similarly there is some integer \(j\) such that \(n = 2j\). We can then write
\[ m + n = 2i + 2j = 2(i + j)\;. \]
The second equality follows from the distributive law of multiplication. So, \(m+n\) can be written in the form \(2k\) for the choice \(k = i+j\). Therefore, \(m+n\) is an integer, as was to be shown.
Draft a proof that the sum of two odd integers is also even. It’s ok not to write out complete sentences, but use abbreviations that would help remind you which sentences to put where.
For more tips, see the guide to Writing Mathematics Well by Francis Su at Harvey Mudd College.