Does x + 0 = 0? What is 1 + 1? Does a + b = b + a? Come find out with me!

Some problems are easy for people but hard for computers! We'll focus on the example of Captchas, where some short text is shown in weird fonts and all twisted up. One of the promising techniques people use to teach computers to solve these problems is called generative modelling. We'll introduce some basic notions from probability and use them to learn how we can teach computers to think!

Come learn about prime numbers! How many are there? How far apart are they? What do they look like? They're hard and boring and nobody cares about them. You probably shouldn't come to this class.

I'll teach as much math as I can in an hour, but will only speak in 14-line sonnets! No, I don't know how this will go either.

Quantum mechanics and special relativity make weird predictions. Space and time can stretch, particles are actually waves, and $$E = mc^2$$! What happens when these two weird things collide? Quantum Field Theory (QFT) that's what! In this course the introductory concepts of quantum mechanics and special relativity will be taught. The course will culminate in a brief intro to the concepts of QFT. By the end of this course we hope that you will have an appreciation for the wonderful word of Quantum Fields.

Donuts aren't spheres. Bubbles are spheres. Lines aren't planes. Four isn't five. Are you sure? Come learn about obvious things and why they're true - but we're certainly not going to be taking the easy route, and we'll learn some cool math in the process!

Let's look at prime numbers as sums of infinitely many complex numbers. No wait! Let's look at them as points on a curve. Actually, let's look at them as an infinite-dimensional space. Wait, is $$1 + i $$ prime? Is there a polynomial that only outputs prime numbers? Leave behind the days when you thought prime numbers were just numbers without any factors. We're not about that "treating numbers as numbers" life.

Matrices are just big squares of numbers and they don't make any sense. I don't understand why you don't just multiply the numbers to multiply matrices, or why anybody would ever want to take a determinant, or what's up with inverses. Maybe if I go to this class, we can learn together.

We'll learn all of math. If we have time left over, we'll talk about applications to other fields.

Can I put my food in a super bowl? Is March Madness some sort of disease? Are the Red Sox an article of clothing? In college life and the real world, one of the central points of social interaction is professional sports, and it's helpful in making friends and career connections to be able to hold up your end of a sporting conversation. Come learn how!

What if we had infinitely big numbers? We could write things like ....99999 = -1, which would make ...11111 = -1/9. Is this ok? Does this break math? Would geometry change? Come find out!

Want to learn about p-adics, but are you worried the other class will make too much sense? Prepare to have your mind blown as we explore: - Balls where every point is the center - Expanding i as an infinitely big integer - Nonzero numbers that you can multiply to make 0 - The best convergence test ever ...and anything else we have time for!

About fifty years ago, Julia Robinson, Yuri Matiyasevich, Hilary Putnam, and Martin Davis together proved a theorem that doesn't make any sense: any set of integers that a computer can understand is the set of positive outputs of some polynomial. What does this mean? It means there's a polynomial whose positive outputs are all prime (and, in fact, are all the primes). There's a polynomial that only outputs Fibonacci numbers. There's another that can output any positive integer except for those whose english spellings contain an even number of vowels. How does that work? Why does that even make sense? Who cares? Come find out with me!

9 out of 10 dentists recommend Sensodyne toothpaste! Colgate Total is the most recommended toothpaste by dentists and hygienists! The average American household makes $60,528 per year (source: US Census), and the average American household makes $44,389 (source, US Census) per year. "Zicam worked to help shorten my cold, an effective and safe product." Geico will save you up to 15% or more on car insurance! In our lives, we're faced with tons of numbers and statistics. A high school or college-level introduction to statistics will teach you a lot about using statistics, but in the real world we're faced with a much different problem: how do you tell which statistics you see you should believe, and which are either trying to mislead you or straight-up lying? In this class, we'll spend some time learning about statistical concepts such as mean, median, mode, standard deviation, normal (and other!) distributions, z-scores, and sampling methods, but we'll focus a lot more on both errors in applying these statistics to come to false conclusions, and ways people misuse them to deceive you. Come learn how to fight back when people lie to you with statistics!

In ancient Greek mythology, the Sphinx was a terrible monster who would ask passing travellers difficult number theory problems. Fortunately, Oedipus defeated the Sphinx when he INVENTED NEW NUMBERS OUT OF THIN AIR. Let's follow in his footsteps to protect ourselves from certain doom! Along the way we'll meet some abstract algebra, some algebraic number theory, and prove some nifty things about ordinary integers. (Example Sphinx questions include finding all integers $$n,k$$ with $$n^7 + 7 = k^2$$ or all primes of the form $$a^2 + 3b^2$$.)

Let's say you're sitting around, and a dragon comes up and threatens to eat you unless you tell him the integral from 0 to infinity of 1/(x^4 + 1) You sit down, and begin trying every possible u-substitution you can think of, but nothing seems to work and you give up. Right before being eaten, you think to yourself "What if there was a super fast way to answer this using complex numbers so I wouldn't have to be eaten by this dragon?" Fortunately, you attended this class and so, with seconds to spare, you yell out "PI DIVIDED BY TWICE THE SQUARE ROOT OF TWO", and the dragon leaves you alone and you also get like a bazillion dollars because that's what happens when you vanquish dragons from kingdoms. Come to this class to see really fast, nifty ways of doing weird integrals and to avoid being eaten by dragons!

One day you buy a pair of rabbits. (Not realizing, of course, that these are killer rabbits). As rabbits are prone to do, this pair grows up and then breeds and suddenly you have more rabbits. As you may know, the number of pairs of rabbits follows the Fibonacci Sequence: 1,1,2,3,5,8, and so on. Then weird things start happening, and you find the equation $$2y^4x + y^3x^2 - 2y^2x^3 - y^5 - yx^4 + 2y$$ etched into the rabbit cage. Weirder still, you try plugging integers into this equation, and notice that when the output is positive, it always seems to be a Fibonacci number. You don't know if explaining why will stop the impending Rabbitpocalypse, but you don't really have any other hope so you'd better come to this class and find out!