ESP Biography



AARON DUNBRACK, Stony Brook Physics Ph.D. Student




Major: Physics

College/Employer: Stony Brook

Year of Graduation: G

Picture of Aaron Dunbrack

Brief Biographical Sketch:

I am a Ph.D. student at Stony Brook. My primary research interest is mathematical physics.



Past Classes

  (Look at the class archive for more.)


Quantum Mechanics Done Right in Splash 2017 (Nov. 18 - 19, 2017)
I'm going to teach quantum mechanics in a way that is both completely accurate and completely comprehensible - sweeping a few details of calculations under the rug, of course. The first half of the class will teach what the world "really is" in quantum mechanics, then how that leads naturally to superposition and the uncertainty principle. The second half will discuss composite quantum systems: we'll start with entanglement, then move on to how that leads to measurement and the different interpretations of quantum mechanics. Given extra time, I have more material I can cover as well.


Conceptual Calculus in Splash 2017 (Nov. 18 - 19, 2017)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Hitchhiker's Guide to the Multiverse in Splash 2017 (Nov. 18 - 19, 2017)
In this class, we will explore three questions. One: What is a multiverse? Two: Why might we want to (or not want to) discuss a multiverse? Three: What are the kinds of multiverses that people talk about? Along the way, we will discuss topics in both modern physics and philosophy.


Multivariable/Vector Calculus in Splash 2017 (Nov. 18 - 19, 2017)
Learn what comes after "regular" calculus. We'll start with vector fields, partial derivatives and multiple integrals and end with an explanation of the gradient, divergence, curl, flux and curvature.


Partial Differential Equations in Splash 2017 (Nov. 18 - 19, 2017)
One of the hardest topics in mathematics is the study of partial differential equations. However, they describe a variety of mechanisms which depend on both position and time, such as fluids, quantum particles, and various biological population models. We will start out looking at transport (including nonlinear transport) and the method of characteristics and move on to diffusion and waves on both bounded and unbounded domains.


Nonlinear Dynamics in Splash 2017 (Nov. 18 - 19, 2017)
This class will serve as a conceptual introduction to understanding the qualitative behavior of differential equations.


Renormalization and Statistical Physics in Splash 2017 (Nov. 18 - 19, 2017)
"Renormalization" is a fancy word that shows up in a lot of high-level physics discussion without nearly as much effort to translate it down to a reasonable level. What is renormalization, really? I'll mainly focus on discussing it in a few statistical mechanics models which make for simpler conceptual understanding, but if I have extra time I'll paint a picture of how it's used in particle physics as well.


Hitchhiker's Guide to the Multiverse in Splash 2016 (Nov. 19 - 20, 2016)
In this class, we will explore three questions. One: What is a multiverse? Two: Why might we want to (or not want to) discuss a multiverse? Three: What are the kinds of multiverses that people talk about? Along the way, we will discuss topics in both modern physics and philosophy.


Quantum Mechanics Done Right in Splash 2016 (Nov. 19 - 20, 2016)
I'm going to teach quantum mechanics in a way that is both completely accurate and completely comprehensible - sweeping a few details of calculations under the rug, of course. The first half of the class will teach what the world "really is" in quantum mechanics, then how that leads naturally to superposition and the uncertainty principle. The second half will discuss composite quantum systems: we'll start with entanglement, then move on to how that leads to measurement and the different interpretations of quantum mechanics. Given extra time, I have more material I can cover as well.


Abstract Linear Algebra and Physical Applications in Splash 2016 (Nov. 19 - 20, 2016)
Most classes on linear algebra are rather dull discussions on how to manipulate matrices. This will not be. We're going to discuss the machine, the language, of linear algebra - as seen by mathematicians and not computer scientists. We'll go through many of the same ideas as a standard linear algebra course - vectors, dot products, linear transformations, eigenvalues, and so on - but do them without reference to matrices. This class will conclude with a discussion of how linear algebra relates to both relativity and quantum mechanics.


Conceptual Calculus in Splash 2016 (Nov. 19 - 20, 2016)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Point-Set Topology in Splash 2016 (Nov. 19 - 20, 2016)
People often think of topology as what surfaces can be smoothly shaped into other surfaces. More generally, topology discusses continuous functions. We'll discuss what it means for a set to have topology, what it means for a function in a topological space to be continuous, and various attributes that a topological space can have.


Partial Differential Equations in Splash 2016 (Nov. 19 - 20, 2016)
One of the hardest topics in mathematics is the study of partial differential equations. However, they describe a variety of mechanisms which depend on both position and time, such as fluids, quantum particles, and various biological population models. We will start out looking at transport (including nonlinear transport) and the method of characteristics and move on to diffusion and waves on both bounded and unbounded domains.


Symmetry in Splash 2016 (Nov. 19 - 20, 2016)
You've surely learned about things which are "symmetric" - which you can do something to and they look the same (e.g., rotating a square by 90 degrees). In this class, we'll discuss how to formalize that idea using the abstract algebra idea of a group, and some specific examples. We'll also discuss how continuous symmetries lead to "conserved quantities" in physics (and what this means).


Multivariable/Vector Calculus in Splash 2016 (Nov. 19 - 20, 2016)
Learn what comes after "regular" calculus. We'll start with vector fields, partial derivatives and multiple integrals and end with an explanation of the gradient, divergence, curl, flux and curvature.


Conceptual Calculus in Spark 2016 (Mar. 12 - 13, 2016)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Point-Set Topology in Spark 2016 (Mar. 12 - 13, 2016)
People often think of topology as what surfaces can be smoothly shaped into other surfaces. More generally, topology discusses continuous functions. We'll discuss what it means for a set to have topology, what it means for a function in a topological space to be continuous, and various attributes that a topological space can have.


Symmetry in Spark 2016 (Mar. 12 - 13, 2016)
You've surely learned about things which are "symmetric" - which you can do something to and they look the same (e.g., rotating a square by 90 degrees). In this class, we'll discuss how to formalize that idea using the abstract algebra idea of a group, and some specific examples. We'll also discuss how continuous symmetries lead to "conserved quantities" in physics (and what this means).


Quantum Mechanics Done Right in Spark 2016 (Mar. 12 - 13, 2016)
I'm going to try to teach quantum mechanics in a way that is both completely accurate and completely comprehensible - sweeping a few details of calculations under the rug, of course. We'll begin by discussing what the world "really is" in quantum mechanics, then interpret that in terms of words like "superposition" and "entanglement." I'll also try to discuss some more advanced topics, like "decoherence," "Hilbert space" and "unitarity." Finally, depending on time, I'll expand on different interpretations of quantum mechanics, including hidden variable, collapse, many-worlds, and information-theoretic formulations.


Hitchhiker's Guide to the Multiverse in Spark 2016 (Mar. 12 - 13, 2016)
In this class, we will explore three questions. One: What is a multiverse? Two: Why might we want to (or not want to) discuss a multiverse? Three: What are the kinds of multiverses that people talk about? Along the way, we will discuss topics in both modern physics and philosophy.


Name That Math! in Spark 2016 (Mar. 12 - 13, 2016)
This is designed to be a class where I (try to) explain the kinds of things covered in just about every math class in college, both undergraduate and graduate school. The idea of this class is that you learn a bunch of basic words in an area of math that you can go google later, with some idea of which ones you find more interesting than others. Extra time (if any) will be spent actually explaining based on student curiosity.


Classical Physics in Splash 2015 (Nov. 21 - 22, 2015)
There's a lot of physics to know even before one gets to the 20th century. I plan to teach all of this physics (one way or another) in two hours. I'll start with some math concepts, then discuss physics. We'll cover: Mechanics (Newtonian, Lagrangian, Hamiltonian ideas), Electricity and Magnetism (Electrostatics, Magnetostatics, and then Electromagnetism), Thermodynamics (Conceptual, Entropy, Types of processes, Gasses), and Waves (traveling, standing, relationships between the two).


Symmetry in Splash 2015 (Nov. 21 - 22, 2015)
You've surely learned about things which are "symmetric" - which you can do something to and they look the same (e.g., rotating a square by 90 degrees). In this class, we'll discuss how to formalize that idea using the abstract algebra idea of a group, and some specific examples. We'll also discuss how continuous symmetries lead to "conserved quantities" in physics (and what this means).


Partial Differential Equations in Splash 2015 (Nov. 21 - 22, 2015)
One of the hardest topics in mathematics is the study of partial differential equations. However, they describe a variety of mechanisms which depend on both position and time, such as fluids, quantum particles, and various biological population models. We will start out looking at transport (including nonlinear transport) and the method of characteristics and move on to diffusion and waves on both bounded and unbounded domains.


Hitchhiker's Guide to the Multiverse in Splash 2015 (Nov. 21 - 22, 2015)
In this class, we will explore three questions. One: What is a multiverse? Two: Why might we want to (or not want to) discuss a multiverse? Three: What are the kinds of multiverses that people talk about? Along the way, we will discuss topics in both modern physics and philosophy.


Conceptual Calculus in Splash 2015 (Nov. 21 - 22, 2015)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Abstract Linear Algebra and Modern Physics in Splash 2015 (Nov. 21 - 22, 2015)
Linear algebra is the most fundamental field of advanced mathematics, central to modern physics. At its core, it is massively simple, yet there is much hidden complexity. In the first third of the class, we will discuss the fundamentals of linear algebra: what are vectors & vector spaces, duals to vectors, linear transformations, and inner products. After that, I'll introduce some concepts from quantum mechanics, and use them to motivate eigenvectors and eigenvalues. I will then use those tools to help you understand what is "really going on" in quantum mechanics. Finally, I'll discuss tensors and special relativity, and then proceed into various other topics based on time.


Quantum Mechanics Done Right in Splash 2015 (Nov. 21 - 22, 2015)
I'm going to try to teach quantum mechanics in a way that is both completely accurate and completely comprehensible - sweeping a few details of calculations under the rug, of course. We'll begin by discussing what the world "really is" in quantum mechanics, then interpret that in terms of words like "superposition" and "entanglement." I'll also try to discuss some more advanced topics, like "decoherence," "Hilbert space" and "unitarity." Finally, depending on time, I'll expand on different interpretations of quantum mechanics, including hidden variable, collapse, many-worlds, and information-theoretic formulations.


Point-Set Topology in Splash 2015 (Nov. 21 - 22, 2015)
People often think of topology as what surfaces can be smoothly shaped into other surfaces. More generally, topology discusses continuous functions. We'll discuss what it means for a set to have topology, what it means for a function in a topological space to be continuous, and various attributes that a topological space can have.


Multivariable/Vector Calculus in Splash 2015 (Nov. 21 - 22, 2015)
Learn what comes after "regular" calculus. We'll start with vector fields, partial derivatives and multiple integrals and end with an explanation of the gradient, divergence, curl, flux and curvature.


Conceptual Calculus in Spark 2015 (Mar. 14 - 15, 2015)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Abstract Linear Algebra in Spark 2015 (Mar. 14 - 15, 2015)
Linear algebra is the most fundamental field of advanced mathematics. At its core, it is massively simple, yet there is much hidden complexity. The first half of the class will be devoted to vectors & vector spaces, duals to vectors, the Hom space and linear transformations, and tensors, all in an abstract sense (with examples, of course). We will then move on to the typical case of Euclidean space: coordinates matrix algebra, determinants, eigenvectors/eigenvalues and their geometric interpretations, and algorithms in linear algebra. Depending on time, we'll discuss some combination of applications to compression algorithms, the relation to special relativity, and functions as vector spaces.


Symmetry in Spark 2015 (Mar. 14 - 15, 2015)
You've surely learned about things which are "symmetric" - which you can do something to and they look the same (e.g., rotating a square by 90 degrees). In this class, we'll discuss how to formalize that idea using the abstract algebra idea of a group, and some specific examples. We'll also discuss how continuous symmetries lead to "conserved quantities" in physics (and what this means).


High-Level Math in a Nutshell in Spark 2015 (Mar. 14 - 15, 2015)
I'm basically going to try to teach all the concepts in all of college math in two hours. I'll start with calculus and linear algebra in the first hour, maybe covering some differential equations if we have time. I'll spend the second hour on a variety of more advanced topics - abstract algebra, complex analysis, topology, manifolds, maybe some measure theory if we have time.


Point-Set Topology in Spark 2015 (Mar. 14 - 15, 2015)
People often think of topology as what surfaces can be smoothly shaped into other surfaces. More generally, topology discusses continuous functions. We'll discuss what it means for a set to have topology, what it means for a function in a topological space to be continuous, and various attributes that a topological space can have.


Many Worlds and Quantum Weirdness in Spark 2015 (Mar. 14 - 15, 2015)
Quantum mechanics has a lot of things about it which are typically thought of as very weird. The first half of the class will be a discussion of various aspects of quantum mechanics: the wavefunction, the uncertainty principle, superpositions, quantization, etc. We will also set up some discussion later by looking the anthropic principle and related notions. The second half of the class will be a discussion oriented around the idea of many worlds. I'll start off by explaining the different types of many-worlds theories, and then we'll conclude with a group discussion about how plausible these options are.


Classical Physics in Spark 2015 (Mar. 14 - 15, 2015)
There's a lot of physics to know even before one gets to the 20th century. I plan to teach all of this physics (one way or another) in two hours. I'll start with some math concepts, then discuss physics. We'll cover: Mechanics (Newtonian, Lagrangian, Hamiltonian ideas), Electricity and Magnitism (Electrostatics, Magnetostatics, and then Electromagnitism), Thermodynamics (Conceptual, Entropy, Types of processes, Gasses), and Waves (traveling, standing, relationships between the two).


Partial Differential Equations in Splash 2014 (Nov. 22 - 23, 2014)
One of the hardest topics in mathematics is the study of partial differential equations. However, they describe a variety of mechanisms which depend on both position and time, such as fluids, quantum particles, and various biological population models. We will start out looking at transport (including nonlinear transport) and the method of characteristics and move on to diffusion and waves on both bounded and unbounded domains.


Multivariable/Vector Calculus in Splash 2014 (Nov. 22 - 23, 2014)
Learn what comes after "regular" calculus. We'll start with vector fields, partial derivatives and multiple integrals and end with an explanation of the gradient, divergence, curl, flux and curvature. Warning: This class will be very fast-paced and it will be likely (expected, in fact) that many things you will feel like you fully understand in-class and then be unable to go back you out of class.


Conceptual Calculus in Splash 2014 (Nov. 22 - 23, 2014)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Mechanics in Three Hours in Splash 2014 (Nov. 22 - 23, 2014)
Learn everything from kinematics to gravity to the rules of rotation in rapid-fire format. This course will move quickly and will have fewer "sample problems" than your high school physics course. Formulas will be given in their most general form, and we won't bother to learn all of the special cases. If we have time at the end, we may delve a little bit into electricity and magnetism.


Programming Concepts in Splash 2014 (Nov. 22 - 23, 2014)
Learn how to write a program, at least in theory. Note that this course will not use any particular language, because languages have syntax, and syntax is annoying. Instead, we are going to learn conceptually how to program in any language, which you can then use in any language you want, whether it’s Python, C, Java, or something else entirely.


Ordinary Differential Equations in Splash 2014 (Nov. 22 - 23, 2014)
Learn how to solve the simplest of differential equations - separable differential equations and linear ordinary differential equations. We will mainly cover homogeneous cases, but I will try to briefly discuss inhomogeneous cases at the conclusion of the class.


The Stuff of the Universe in Splash 2014 (Nov. 22 - 23, 2014)
Want to know what the universe is made of? Not just the usual protons, neutrons, and electrons either - more exotic matter as well. I'll cover the Standard Model and the kinds of particles that arise from it, and why they occur. I'll then cover particles that aren't in the Standard Model - which covers the main present theories of dark matter and energy.


Cosmology: The Early Universe in Spark 2014 (Mar. 15 - 16, 2014)
Ever wondered what the early universe looks like? How the early atoms formed? What happened at the big bang? And, equally if not most importantly, how do we know all this stuff?


Rapid-Fire Mechanics in Spark 2014 (Mar. 15 - 16, 2014)
Come to get a rapid overview of mechanics. We'll go over kinematics, forces, momentum, energy, Galilean relativity, gravity, rotational dynamics and angular momentum. If we have time, we'll discuss classical thermodynamics, some electricity and magnitude, and special and maybe even general relativity.


Philosophy of Science in Spark 2014 (Mar. 15 - 16, 2014)
What is science? What are the assumptions we make when we do science? What is the interaction between science and religion? What is the relationship between science and philosophy in general? We'll go over these questions in a discussion-style format that should be thought-provoking and interesting.


Philosophy of Mathematics in Spark 2014 (Mar. 15 - 16, 2014)
We do a lot with math today, and math has done a lot with science. But how can we be sure that math is "right," so to speak? I'll talk about some of the abstract bases of mathematics, specifically some abstractions of set theory and logical argument, and then you'll get to debate one of the most fundamental questions of mathematics (with me, if everyone takes the same side): is mathematics created or discovered?


Conceptual Calculus in Spark 2014 (Mar. 15 - 16, 2014)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Programming Concepts in Spark 2014 (Mar. 15 - 16, 2014)
Learn how to write a program, at least in theory. Note that this course will not use any particular language, because languages have syntax, and syntax is annoying. Instead, we are going to learn conceptually how to program in any language, which you can then use in any language you want, whether it’s Python, C, Java, or something else entirely.


Introduction to Dungeons and Dragons in Splash! 2013 (Nov. 23 - 24, 2013)
Have you always wanted to play Dungeons and Dragons, or at least try it out, but never knew what it was? This is definitely the class for you! Learn how to play and be able to teach your friends at home. I’ll give an overview of the game, an explanation of the relevant rules, and a look at how to lead a game, and (if we still have time) we'll either create characters or play through a sample dungeon.


Dungeons and Dragons Optimization (3.5) in Splash! 2013 (Nov. 23 - 24, 2013)
In short: you know how to play. Now learn how to talk with experienced gamers about things like RAW vs. RAI, Pun-Pun v. the Omnicifier, the d2 Crusader v. a mailman sorcerer, and the tier system. (Note: if you've been a lurker on just about any RPG forum, you'll probably already be conscious of what will be taught in this class.)


Non-DnD RPG Systems in Splash! 2013 (Nov. 23 - 24, 2013)
Ever heard of GURPS, Burning Wheel, Mouse Guard or Paranoia? Haven't, but want to? Have, but want to learn more? Then this class is just what you want to take.


Mechanics in Three Hours in Splash! 2013 (Nov. 23 - 24, 2013)
Learn everything from kinematics to gravity to the rules of rotation in rapid-fire format. This course will move quickly and will have fewer "sample problems" than your high school physics course. Formulas will be given in their most general form, and we won't bother to learn all of the special cases. If we have time at the end, we may delve a little bit into electricity and magnetism.


Conceptual Calculus in Splash! 2013 (Nov. 23 - 24, 2013)
Learn what it means to take the limit, the derivative, or the integral! Also learn how to apply these concepts in some pretty cool ways. Note: this class will be almost entirely conceptual - very few actual derivatives will be taken, although some of the more interesting ones may be used.


Multivariable/Vector Calculus in Splash! 2013 (Nov. 23 - 24, 2013)
Learn what comes after "regular" calculus. We'll start with vector fields, partial derivatives and multiple integrals and end with an explanation of the gradient, divergence, curl, flux and curvature. Warning: This class will be very fast-paced and it will be likely (expected, in fact) that many things you will feel like you fully understand in-class and then be unable to go back you out of class.


Programming Concepts in Splash! 2013 (Nov. 23 - 24, 2013)
Learn how to write a program, at least in theory. Note that this course will not use any particular language, because languages have syntax, and syntax is annoying. Instead, we are going to learn conceptually how to program in any language, which you can then use in any language you want, whether it’s Python, C, Java, or something else entirely.


Working with Databases in Splash! 2013 (Nov. 23 - 24, 2013)
Learn the basics of working with databases - mainly SELECT, UPDATE and DELETE - using SQL. We'll go over advanced topics such as joins if we have time.


Color Physics! in Splash! 2013 (Nov. 23 - 24, 2013)
Ever wondered why red and yellow light make orange, or why there are three primary colors? Come here to learn why! (Hint: It has less to do with physics - and more to do with how your eyes work - than you think.) We'll talk a bit about random tidbits about color as well if we have time.