Love of Math

Join us for the Spring 2027 Semester in

Introduction to Proof (University Level)

Tuition: $1250 for the semester

January 8, 2027 -
May 28, 2027

Live meetings
Tuesdays and Fridays
11:45am-1:00pm ET

This course relies primarily on one of the textbooks below: 
* "Book of Proof" by Hammock,
* "How to Prove It" by Velleman, or
* "Proofs and Fundamentals" by Bloch
(TBD)

What's included?

  • Live, interactive zoom meetings twice a week where we work out the important details of each topic together (sessions will be recorded and videos posted for later viewing as well)
  • Weekly live office hour with Dr. Finotti, and a second hour available on request 
  • Written homework sets with instructor written feedback, with careful choice of exercises in order to allow students sufficient practice for full mastery and retention without falling into "drill and kill" over-repetition.
  • The choice between a graded track (where the instructor issues a letter grade at the end of the course) and a non-graded certificate of completion track (where I do not issue a letter grade)
  • Periodic exams given throughout the course to assess mastery and identify any areas needing further study. (Exams are optional on the Certificate of Completion Track)
  • Students can submit corrections on all homework (and on midterm exams for reduced credit back), to keep the focus on mastery rather than grades.

Rigorous Small Group Class

With a class size capped at 12 students, we'll lay a strong foundation in this critical course. Through our live, interactive classes, we'll delve deep into the fundamentals at the heart of proof construction while exploring some of math's most intriguing and beautiful ideas. 

Our intention is always to create a growth focused, supportive, mistakes-embraced environment with the appropriate level of challenge to keep our students growing. That said, this class is not a "fluffy" course. It is designed for students that don't need much repetition, have high motivation for learning math, and are ready for a university level, rigorous, introduction to proof course. 

Students need to have completed a complete year of university level Calculus in order to take this course but do not need to have had any other further particular coursework.  However, because of the level and rigor of the content, a certain level of "mathematical maturity" is also needed.  Students that have grown up on the AoPS materials and had a very rigorous Calculus course are typically well suited for this class, as they've already had lots of exposure to some of the logical foundation needed for good proof construction.  It is important that students are already also comfortable showing on paper and thoroughly explaining their mathematical thought processes. 

Please note the content is designed as a university level course, moves at a (fast) university course pace, and is presented at a university level of rigor. If you have any concerns about whether or not your student is ready for this course, please contact me through our Contact Page form.

Why take Intro to Proof?

In universities, this type of course generally serves as a bridge between the typical freshman/sophomore university level math courses (Multivariable Calculus, Differential Equations, Linear Algebra) and all of the upper level proof-focused courses (Real Analysis, Modern Algebra, Topology, etc).  But for students that have the necessary "mathematical maturity", there is really no reason to wait so long to set a solid foundation in all things proof! 

The honing of one's logical skills is invaluable in mathematics, but also in other areas of study as well as in day-to-day life.

In his autobiography, Charles Darwin wrote: "During the three years which I spent at Cambridge… I attempted mathematics… but got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for [people] thus endowed seem to have an extra sense."  It is exactly this careful construction of good logical skills that I suspect led to that "extra sense" that Darwin noted. It changed my life immeasurably to build those skills, and I've had the great fortune to watch students walk through similar transformations and share with me the impact that it had on their lives outside of mathematics. 

As we build these valuable logic skills,  along the way we'll get to deepen and expand our understanding of  various ideas in counting, number theory, Calculus, sets and relations on sets, the structure of the real numbers, and the concept of infinity. 
Meet the instructor

Dr. Heather Finotti

This course material stands out to me as one of the most transformative for students of all the math courses I have ever taught.  Students often come away from the course noting that not only have they learned new mathematical content and skills, but their thinking in their day-to-day life has shifted.  They read the news differently, argue differently, think more thoroughly and carefully. Many in the past remarked that they wish it was the first math course they took in college, because it allowed them to read mathematics more easily and with more depth of understanding. I am very excited when I have the opportunity to teach it! 
Patrick Jones - Course author
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