The math department will expand its course offerings with the addition of Introduction to Proofs Honors, a new elective, in the 2026-27 school year. This senior-only course aims to help students explore math beyond traditional algebra and calculus-centered topics, with topics including proof by disjunction, quantifiers and formal logic. The class also introduces multivariable calculus concepts in the final quarter, justifying the prerequisite of being concurrently enrolled in an AP calculus class to ensure preparedness.
Developed by math teacher Misha Hlasek and Math Instructional Lead Daniel Hahn, the curriculum is focused on the reasoning and structure behind mathematical reasoning, concepts that aren’t typically taught until college.
“The other math electives (at Gunn) include Applied Math H and AP Statistics, both of which are very real-world,” Hlasek said. “That is not what proofs are. Proofs are the most beautiful, elegant, abstract and theoretical (math topic). It gives you the foundation for all the other math (topics) there.”
The course is also designed to bridge the gap between high school math and college proof courses.
“Some (college proof courses) will just dive into the math, hoping that you will observe the proof techniques from what’s going on,” Hlasek said. “We want to give you a foundation so that when that happens to you in college, you can be like ‘Yeah, I know what that is.”
Unlike other weighted courses in the traditional math pathway, this class will emphasize a revision-based learning system that shifts focus away from performance under pressure, aligning the course structure more closely with the problem sets-heavy approach used in the Applied Math elective.
“(Using that structure), we’d then ultimately lead to you having the skill of fine-tuning a proof rather than there being a timed assessment,” Hlasek said.
The curriculum is based around Daniel J. Velleman’s textbook “How to Prove It: A Structured Approach.” In it, topics ranging from derivation techniques such as contradiction and induction to set theory are covered. The book was specifically selected for its unique step- by-step approach to explaining proof systems and mathematical argumentation.
“One thing I really really like about it, and I haven’t seen it anywhere else throughout my own studies, (is that) it has a scratch work section, which shows what it actually looks like when a person sits down and starts thinking about proof,” Hlasek said.
Intro to Proofs replaces the once-expected Multivariable Calculus course after contentious discussions over whether adding another advanced class would increase academic pressure for students. According to Hahn, surveyed honors students reported feeling less obligated to take Intro to Proofs than Multivariable Calculus.
“Comparing this class to Multivariable Calculus, the number of students that said they would be pressured to take Intro to Proofs was far less,” he said. “(The) pressure to take Multivariable Calculus if it was offered was upwards of 86% in the Honors lane, which was more confirmation for me that it would be the wrong direction to take (for) the math department.”
Junior Hanting Liu, who first heard about the elective from Hlasek in class, signed up during course selection to strengthen his skills in more abstract areas of math.
“I heard that this class will cover the more theoretical side of math, which is different and something I want to improve on,” he said. “I’m mainly taking this class for myself (rather than for college) so that I can explore and learn something new.”
