Nick Rauh

BS, Harvey Mudd College. PhD, University of Texas. Areas of expertise include number theory and recreational mathematics. Former chief of mathematics, National Museum of Mathematics. Previously taught at University of Texas and Texas State University. SLC 2017–

Undergraduate Courses 2019-2020

Computer Science

Computational Number Theory

Open , Seminar—Spring

Number theory is one of the oldest and most beautiful fields of mathematics, and many of the ideas it has generated over the millennia are just now becoming crucially important in the information age. This course will serve as an introduction to number theory, computer programming, and the interplay between the two. Topics will include divisibility, prime factorization, modular arithmetic, cryptography, and algorithms, with other topics selected based on class interest. We will spend some time formulating conjectures, generating evidence to support or disprove them, and attempting to prove the ones that seem true. We will also address algorithmic questions such as run-time efficiency and compare and contrast different mathematical algorithms that theoretically achieve the same goal but differ practically in consequential ways.

Faculty
Related Disciplines

Mathematics

Calculus II: Further Study of Motion and Change

Open , Seminar—Fall

Prerequisites: one year of high-school calculus or one semester of college-level calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the spring semester of this academic year.

This course continues the thread of mathematical inquiry following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, infinite series, and power series representations of functions. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study of some other mathematically-related topic. This seminar is intended for students interested in advanced study in mathematics or sciences, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind. The theory of limits, differentiation, and integration will be briefly reviewed at the beginning of the term.

Faculty

Multivariable Mathematics: Linear Algebra, Vector Calculus, and Differential Equations

Intermediate , Seminar—Year

Prerequisite: successful completion of Calculus II or a score of 4 or 5 on the AP Calculus BC exam.

This yearlong course will cover the central ideas of linear algebra, vector calculus, and differential equations from both a theoretical and a computational perspective. These three topics typically comprise the intermediate series of courses that students study after integral calculus but before more advanced topics in mathematics and the sciences. This course will be especially meaningful for students interested in pure or applied mathematics, the natural sciences, economics, and engineering but would also be a great choice for students who have completed the calculus sequence and are simply curious to see how deep the rabbit hole goes. While our focus will be primarily on the mathematics itself, the tools we will develop are useful for modeling the natural world—and we will look at some of those applications. Conference work will revolve around pursuing the theory or application of those topics on a deeper level, according to students' personal interests.

Faculty

Previous Courses

Calculus I: The Study of Motion and Change

Open , Seminar—Spring

Prerequisites: the minimum required preparation for study of the calculus is successful completion of study in trigonometry and precalculus topics. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible. This course is also being offered in the fall semester of this academic year.

Our existence lies in a perpetual state of change. An apple falls from a tree; clouds move across expansive farmland, blocking out the sun for days; meanwhile, satellites zip around the Earth transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe and study the motion and change happening around us. The Ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual processes of differentiation and integration. Numerous applications of the theory will be examined. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study of some other mathematically-related topic. This seminar is intended for students interested in advanced study in mathematics or sciences, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind.

Faculty

Calculus II: Further Study of Motion and Change

Open , Seminar—Fall and Spring

Prerequisite: one year of high-school calculus or one semester of college-level calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible.

This course continues the thread of mathematical inquiry following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, and power series representations of functions. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study in some other branch of mathematics. This seminar is intended for students interested in advanced study in mathematics or science, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind. The theory of limits, differentiation, and integration will be briefly reviewed at the beginning of the term.

Faculty

Calculus I: The Study of Motion and Change

Open , Seminar—Fall

Prerequisites: successful completion of trigonometry and pre-calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible.

Our existence lies in a perpetual state of change. An apple falls from a tree; clouds move across expansive farmland, blocking out the sun for days; meanwhile, satellites zip around the Earth, transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe and study the change that we see. The ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual of differentiation and integration. Numerous applications of the theory will be examined. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study in some other branch of mathematics. This seminar is intended for students interested in advanced study in mathematics or science, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind.

Faculty

Calculus I: The Study of Motion and Change

Open , Seminar—Spring

Prerequisites: successful completion of trigonometry and pre-calculus. Students concerned about meeting the course prerequisites are encouraged to contact the instructor as soon as possible.

Our existence lies in a perpetual state of change. An apple falls from a tree; clouds move across expansive farmland, blocking out the sun for days; meanwhile, satellites zip around the Earth, transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe and study the change that we see. The ancient Greeks began a detailed study of change but were scared to wrestle with the infinite; so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual of differentiation and integration. Numerous applications of the theory will be examined. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study in some other branch of mathematics. This seminar is intended for students interested in advanced study in mathematics or science, students preparing for careers in the health sciences or engineering, and any student wishing to broaden and enrich the life of the mind.

Faculty