Welcome to CSCI 0200!

Math Foundations of Computing, F25

Prof. Phil Chodrow
Department of Computer Science
Middlebury College

Plan for Today

Why Math?

How This Class Works.

Breaks throughout for getting to know each other.

Who’s In the Room?

Go to menti.com

Enter code 5178 9074

Respond to the first prompt.

Keep the tab open – we’ll come back to it

Soooooo

…a math class

…in the CS department

…?

CS and Math Go Way Back

Ada Lovelace was an English mathematician and author of the first published computer program (1840).

Her program was designed to compute an important sequence of mathematical constants on the “Difference Engine” designed by Charles Babbage.

Babbage never completed his Difference Engine, so Lovelace’s program was never run.

Lovelace described her approach to math as “poetical science.”

Ada King, Countess of Lovelace. Portrait possibly by Alfred Edward Chalon, image from Wikipedia.

CS and Math Go Way Back

Alan Turing was an English mathematician who played a major role in developing the theory of computer science and AI.

Turing proved that some tasks are impossible for algorithms to perform, no matter how powerful or clever they are.

The “Nobel Prize in Computer Science” is named the Turing Award.

Turing was chemically castrated as a punishment for homosexuality in 1953. The UK managed to apologize for this in…2009.

CS and Math Go Way Back

John von Neumann was a Hungarian mathematician who guided the development of the first digital computers.

The “von Neumann architecture” remains the high-level architectural basis of the design of modern computers.

If you’re wondering what the first digital computers were used for, watch Oppenheimer. 😬😬😬

Ok, but…

…what is mathematics?

Mathematics is the heart of AI and data science

Brin, Sergey. “The PageRank citation ranking: bringing order to the web.” Proceedings of ASIS, 1998 98 (1998): 161-172.

Mathematics is the heart of machine learning

Support Vector Machine (SVM) is an algorithm for classifying data into groups based on past observations.

Deisenroth, Faisal, and Ong (2020). Mathematics for Machine Learning

Mathematics is the heart of algorithmic problem-solving

Dijkstra’s algorithm finds shortest paths between points in a graph.

(Used for e.g. vehicle routing)

Math Foundations: What You Need Now To Do All That Stuff Later

Math and Us

Respond to the second prompt on the Menti poll.

If you closed the tab, go to menti.com and enter code 5178 9074.

In This Class, You Will…

…build a mathematical toolbox for reasoning theoretically about data structures, algorithms, and the world around you.

…test mathematical theory against computational experiments.

…cultivate a joyful relationship with the practice of mathematics.

The Big Picture

mindmap
  root((CSCI 0200))
    )**Module 1**(
        (Logic)
          (Propositional logic)
            (Boolean algebra)
            (Circuit design)
        (Sets)
            (Set Operations)
            (Logical quantifiers)
    )**Module 2**(
        (Relations)
            (Functions)
            (Equivalence Relations)
        (Proof Techniques)
            (Direct)
            (Indirect)
            (Contradiction)
            (Induction)
                (Weak)
                (Strong)
    )**Module 3**(
        (Counting)
            (Sum and product principles)
            (Permutations and combinations)
            (Combinatorial proofs)
        (Recurrence Relations)
            (Asymptotics)
            (Divide and combine)
    )**Module 4**(
        (Probability)
            (Distributions)
                (Conditioning)
            (Random variables)
                (Expectation)
        (Graphs)
            (Special graphs)
                (Trees )
                (Cycles)
            (Algorithms)

Your Affinity Vegetable

1. Split into teams

2. Go around and share your name and:

If you were a vegetable, which vegetable would you be and why?

Your Affinity Vegetable

3. Team leader: lead your team in finding a delicious dish that incorporates all of your vegetables.

Be ready to share!

This is a flipped classroom.

In a flipped classroom, you complete readings and watch lectures before our scheduled class time.

A Typical 3-Week Module

gantt
    title A CSCI 0200 Module
    axisFormat %A
    tickInterval 1day
    section Week A
    Prep, warmup            :active, a1, 2014-01-06, 1d
    Class            :2014-01-06, 1d
    Prep, warmup         :active, a2, 2014-01-08, 1d
    Class         :2014-01-08, 1d
    Prep, warmup    :active, a1, 2014-01-10, 1d
    Lab A           :a3, 2014-01-10, 1d
    section Week B
    Prep, warmup            :active, a1, 2014-01-06, 1d
    Class            :2014-01-06, 1d
    Prep, warmup         :active, a2, 2014-01-08, 1d
    Class         :2014-01-08, 1d
    Prep, warmup    :active, a1, 2014-01-10, 1d
    Lab B           :a3, 2014-01-10, 1d
    Lab A due         :done, b3, 2014-01-10, 1d
    section Week C
    Prep, warmup            :active, b1, 2014-01-06, 1d
    Class            :2014-01-06, 1d
    Prep, warmup         :active, b2, 2014-01-08, 1d
    Class            :2014-01-08, 1d
    Lab B due         :done, b3, 2014-01-10, 1d
    Quiz              :crit, done, c3,  2014-01-10, 1d

Mondays and Wednesdays

Before Each Class (1.5-2 hrs)

• Prep: Videos and readings
• Warmups: practice problems, graded on completion

In Class (~1 hr)

• Questions
• Group work
• Activities
• Additional topics, demonstrations, etc.

Friday Labs

• 7 total throughout the semester
• Start in class with assigned groups
• Finish as homework and submit a week later

Assessment

Assessed as Excellent (E), Meets Expectations (M), Needs Revision (R), or Not Complete (N). You want Es and Ms.

Revision

You can revise and resubmit your labs after your first assessment in order to achieve a higher assessment.

Quizzes

• Proctored 😩
• 4 total, on Fridays
• Timed for 45 minutes (contact me with DRC letters!!)

Learning Targets

• We have 20 Learning Targets related to core course competencies.
• You’ll have multiple opportunities to complete each Learning Target, but you only need to do it once.
• 4-6 targets are added on each quiz, but you only need to attempt ones you haven’t already gotten.

Final Exam

Includes opportunities to complete all 20 learning targets, with 3 hours.

Tier	Learning Targets	Labs
A	▢ ▢ ▢ ▢	E: ▢ ▢ ▢ ▢ M: ▢ ▢ ▢
B	▢ ▢	E: ▢ ▢ M: ▢ ▢ ▢ ▢ R: ▢
C	▢ ▢	M: ▢ ▢ ▢ ▢ ▢ R: ▢
D	▢ ▢ ▢ ▢ ▢ ▢ ▢ ▢ ▢ ▢	M: ▢ ▢ ▢ ▢

Participation

I structure class so that your presence contributes to your learning and the learning of your peers. So, I expect you to attend and participate in class.

Everyone starts the semester with 6 participation “passes.”

• Miss a warmup activity = 1 pass.
• Skip class (or more than 10 minutes late) = 1 pass.

Using more than six passes starts to affect you grade; see the syllabus.

Screen Free Zone

Starting Wednesday, no screens in class except for Friday labs (or LOAs).

Exceptions for illness, family emergencies, Dean’s Notes, and at my discretion on a base-by-case basis.

Support Resources

Academic support

• Student Hours are your time. I’m sending around a poll to help schedule Student Hours at a time that works for you.
• Evening Peer Help, hours TBD.
• Our Assistant Laboratory Instructor Smith Gakuya holds Student Hours for CSCI 0200.
• EdStem: Online Q&A forum.

Clearing barriers to learning

• The DRC can help you obtain a letter of accommodation for timed assessments.
• Legally, I need your letter in order to offer you accommodations.

For Wednesday

Entrance Survey: tell me about yourself and help me find your teammates for lab.

Student Hours Scheduling Poll: let me know when you’re available for Student Hours.

Math Autobiography: your history as a learner and user of mathematics.

These assignments are on Canvas.