Mathematical Logic

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Mathematical Logic
Math Course
Course CodeREAS
Year Opened1987*
Sites OfferedLOS, SCZ
Previously OfferedCAR, CLA, CLN, HKU, JHU, LAN, RED, SAR, TOW, UNI
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Course Description

From the CTY Catalog:

Have you ever wondered what real mathematicians spend their time doing? This course will teach you the art of proving and disproving conjectures, and techniques for writing formal proofs and counterexamples. You’ll learn key concepts of logic, including validity, soundness, consistency, and satisfiability, and techniques for developing systems of logic in formal symbolic languages. You’ll test the validity of arguments, write precise formal proofs, and explore the rules of grammar and meanings behind the symbols. Then you and your classmates will engage in the process of metalogic, or reasoning logically about a system of logic. You’ll examine soundness and completeness, and along the way, you’ll become proficient at writing proofs accurately and rigorously, a skill essential to career mathematicians. Most importantly, you’ll develop strong problem-solving skills and learn to think analytically—traits vital for rigorous inquiry in any field.

The curriculum of Mathematical Logic varies between years and sites. Common topics include:

  • Formal logical operators such as implication, negation, "and", and "or";
  • Translations
  • Methods of proof, including direct proof, proof by contradiction,
  • Mathematical problem solving;
  • First-order logic;
  • Set theory;
  • Metalogic
  • Intro to Topology (if given Mr. P)
  • Turing, Gödel(if give by Hakim)

Class History

Mathematical Logic is often populated with Squirrels, as its only prerequisite is Algebra I. At LAN, it is often taught by Jake, who is delightfully overenthusiastic, owns stilts, and often does circus tricks. If you have Jake for REAS, make sure to get lots of circus tricks and the mathematics of juggling!At HKU,if you have Hakim for REAS,you definitely have lots of fun.


JHU.11.1: The awesome TA Grace (who does extreme sudokus in under 10 minutes) is now called Graceta. The awesome instructor, John (who is a BEAST) is now called IJohn. The RAs were Ryan (RaRyan) and Angel (who did not have a nickname) We had the best session ever with sentential logic, quantified logic, circuit logic, mathematical induction, proofs, paradoxes, and logic puzzles. We used forallx, and with our awesome class and course, we were an AWESOME class.

The winning logic groups were the Ninjas, Unicorns FTW!, and Vegan Lamposts

JHU.10.1: With the Puzzle Master as a TA, and God of Logic/Harry Potter as a teacher, we had the greatest class ever! Popular break activity was playing with teacher's frisbee. Used textbook forallx. Class included sentential logic, quantificational logic, Aristotlean logic, proofs, and logic puzzles.

JHU.18.1: Class was taught by Teacher John and TA Celeste. We learned about proofs, truth tables/trees, sentential logic, and quantificational logic. We would also do things like Adventures in Paradox Land, logic puzzles, making our own logic puzzles, and Sudoku. During breaks there would usually be a game of Frisbee going on, a few people would talk to Celeste about things like soccer and the sinkholes randomly appearing around campus, however hitting the volley-ball around in a circle was the more popular choice.


LAN.18.2 Honor code is the way (Do you want to be a daddy):

The teacher was Jacob Pichelmeyer (Mr. P, an icon forever and ever) memorable for his tattoo sleeves. After light online stalking he was found to have a history at Star Wars conventions. The following year Mr. P founded the Topology course offered at Lancaster 19.1 and San Francisco 19.2. The TA, Mr. D, was also pretty cool. There was an extensive list appended to during the session referencing his name starting with "D".

There were 9 girls and 6 boys (shocking for a math course (but the guys didn't mind)). The honor code was drilled into the minds of these youngsters and everyone at some point or another had to write a self-reflection about how they had broken it (This is disputed. Some believe the essay we wrote was explaining our interpretation of the honor code, which is a generally in the spirit of the honor code itself). Overall the class was very close and a family tree was created at the end of the session. Avalon and Mr. P's rapping was a highlight of the class and trying to figure out who was hotter, Mr. P or Mr. D was often on the minds of the class, boys and girls alike (the answer is always Mr. P (But really really early in the morning this was a less definite answer)).

The class did generally well at learning all concepts in class.

Avalon was more than just a game played inside and class and out - it is a lifestyle. The guy's hall (Aaron's Hall [Greatest Hall]) decided to make their own paper copy of the game, and they played it most days after it was introduced in class.

LAN.17.1: This was hella lit.

Those involved in the REAS lore: Exia (author), Ashton, Rachel, Niko, Andrew, Cade (Chade), Michelle, Dora, Kuralay (Kuka), Dan, Ethan, Rawley, Evan (Lemon Boy), and Tim. Mr. P was the instructor. He had tattoos all over his arms, mesmerizing the class for the first week. We got used to it eventually. Mr. Matt was the TA. He liked to remind the class of the honor code. An eager 5-year old in an adult body. Too pure for this world. Ellen was the girls' RA. It was her first year as an RA and was overwhelmed most of the time, understandably. (Have a nice day.) Asher was the boys' RA. What a legend.

Godel, Escher, Bach (lovingly/hatefully referred to as "GEB" with a hard g) was often read during the evening class sessions. Almost everyone internally groaned, some externally groaned.

Salty chocolate milk is an abomination on society. Thanks Andrew.

More to be added shortly.

LAN.08.1 G-Farbism:

Using the book Deductive Logic, by Warren Goldfarb, the students began to worship Goldfarb, calling him G-farb for short. The religion is dead to most of Math Logic students, but G-Farb is still alive in our hearts.

LAN.06.2 Total War:

In 06.2, a war between Number Theory and Math Logic erupted. The Math Logic teacher ("What's a mattababy?" "I dunno, baby, what's a matter which you?") instructed his students to chant "PROOF PROOF PROOF" to get revved up. Soon, the Number Theory students also started chanting in their classroom for all to hear. The war eventually evolved to include Etymologies. See the Lancaster Hall of Fame for more information.

In 09 and 10, both sessions, Math Logic was taught by an instructor named Jake that enjoyed circus tricks. The course was very well-taught and included lots of fun activities. The class also got to hear a lot about juggling.

In 11.2, Jake again taught Math Logic along with his awesome TA Josh. The class was a huge amount of fun, but no circus tricks to be seen (hmm...) Jake would have 3 bananas a day, and would boil water in class to make tea or coffee. There were so many proofs, and proof trees to make all day! In 2011, the three logic classes plus Math Logic got together to play proof golf in Mayser! The results were as follows: 1st place: Logic C 2nd place: Logic B 3rd place: Math Logic 4th place: Logic A. At then end of the session, Math Logic watched Inception!

Los Angeles

LOS 17.2: LOS 17.2 Math logic was taught by Joseph Tanner Slagel (who went by Tanner) and a cool TA Celeste. The class was self-proclaimed superior to the other logic class and owned them in every way possible at Proof Golf. The hardcore proof sessions were punctuated by frequent breaks which were filled with violent and merciless 9 Square. The athletes consisted of the Ignorant Texan, Bob the Minion (and the rest of the minions), Isaac the forced King, and the also self-proclaimed great king Nils the Norwegian. As well as some minor players including Elaine, Ayla, Sloan, the Spaniard, Gina the Korean and victim Matthew who was unintentionally targeted every round. As shown, the class was very egotistical. Night sessions were filled with rushed worksheets, numerous rounds of I LOST THE GAME, Set, Butt (dubbed Bottom), BS (shenanigans), and illegal Poker with spectacular final all-in rounds. Going to see the unreal sunset accompanied by sad music became a regular past time. Truth tables were first taught but then came truth trees then natural deduction much to the students’ dismay. Tanner, a huge fan of natural deductions and truth trees, attempted to convince the class of its superiority. Everybody understood that this was pure hypocrisy, and had no utility beyond occupying the students. Tanner was a deeply philosophical man. He spent a lot of his time motivating us with quotes such as: "Be the change you want to see in the world.” A lot of students followed this trend, creating their own quotes such as "contradiction and negation bring you one step closer to the goal" by Magician Matthew. The math logic class became a family by the end of the three weeks, with the glowing last sunset still alive in everyone's hearts.


19.1:In this year,it is taught by Hakim,which doesn't require books but only your notebook.He always let us listening lots of worksheets.The Achilles and the Tortoise is the best drawing ever.Everyday would have a brainteaser and often says'Here is my favourite brainteaser'.The post-accessment is nearly the same as pre-accessment.The weekly class presentation is definitely the best ever.Hakim and Anthony,the TA ,glows in HKU 19.1 REAS class's hearts.