## MATH 100. Intermediate Algebra

**Instructor(s):**
Staff

**Required text(s):**
McCallum, Connally, Hughes-Hallett et al. Algebra: Form and Function. 2nd edition. (with WileyPlus ebook)

**Textbook notes:**
Students buying used textbooks should arrange to purchase WileyPlus separately. Instructions for students to obtain the e-book and to use WileyPlus: use your Loyola email address to create a WileyPlus account. Your professor will include details on WileyPlus in the syllabus.

**Prerequisites:**
None

**Course description:**
Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

**Syllabus:**
Common

## MATH 108. Real World Modeling

**Instructor(s):**
Staff

**Required text(s):**
Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed. *For All Practical Purposes: Mathematical Literacy in Today's World*. 9th ed. ISBN-13: 978-1429243162. New York: W. H. Freeman, 2011. Print.

**Prerequisites:**
None

**Course description:**
An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.

**Syllabus:**
Common

## MATH 117. Precalculus I

**Instructor(s):**
Staff

**Required text(s):**
Eric Connally, Hughes-Hallett, D., and Gleason, A. M. *Functions Modeling Change: A Preparation for Calculus*. 5th ed. New Jersey: Wiley, 2015. Packaged with WileyPlus.

**Prerequisites:**
Math 100 or Math Diagnostic Test

**Course description:**
Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.

**Syllabus:**
Common

## MATH 118. Precalculus II

**Instructor(s):**
Staff

**Required text(s):**
Eric Connally, Hughes-Hallett, D., and Gleason, A. M. *Functions Modeling Change: A Preparation for Calculus*. 5th ed. New Jersey: Wiley, 2015. Packaged with WileyPlus.

**Prerequisites:**
MATH 117 or Math Diagnostic Test

**Course description:**
Functions and change with an emphasis on linear, quadratic, exponential, and logarithmic functions and their graphs. Specific geometric topics include concavity and how transformations affect graphs. Topics in trigonometry include radians, sinusoidal functions, identities, sum/difference formulas, double/half angle formulas, and trigonometric equations. Other topics include polar coordinates.

**Syllabus:**
Common

## MATH 123. Special Topics

**Instructor(s):**
Mr. Marius Radulescu

**Required text(s):**
None

**Recommended text(s):**
Dwyer, David, and Mark Gruenwald. Calculus Resequenced for Students in STEM, Preliminary Edition. Wiley, 2017. ISBN-13: 978-1-119-32159-0

**Prerequisites:**
Department consent required

**Course description:**
A freshman/sophomore seminar designed as a corequisite course for MATH 162 and MATH 263.
The main goal of the course is to provide a rigorous transition from MATH 131 to MATH 162 and from MATH 132 to Math 263. The focus is on new topics from MATH 161 (Calculus I) and MATH 162 (Calculus II) that are required in MATH 162 and MATH 263, respectively, but are not covered in MATH 131/132. The format of the seminar is focused on problem solving on assigned topics.
Students will be graded based on homework and quizzes. There is no final exam for this class.

## MATH 123. Freshman/Sophomore Seminar

**Instructor(s):**
Mr. Marius Radulescu

**Required text(s):**
None

**Prerequisites:**
None

**Course description:**
This one-credit seminar is designed for freshman and sophomore students who are interested in mathematics, whether or not they intend to major or minor in the subject. It will include activities and presentations facilitated by a number of faculty members. These will cover a wide variety of ideas and applications of mathematics, largely chosen from outside the traditional precalculus-calculus sequence.
Students are expected to participate actively, and classes will often include group problem-solving or reflection sessions. It aims to be informal and thought-provoking, and to provide a glimpse into the wider world of math that we in the math and stats department all love.
There are no exams, and grades will be based on participation and occasional written homework.

## MATH 131. Applied Calculus I

**Instructor(s):**
Staff

**Required text(s):**
Hughes-Hallett, Deborah, et al. *Applied & Single Variable Calculus for Loyola University Chicago, Custom* (WileyPlus eBook).

**Prerequisites:**
MATH 118 or Math Diagnostic Test

**Course description:**
An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for MATH 161.

**Syllabus:**
Common

## MATH 132. Applied Calculus II

**Instructor(s):**
Staff

**Required text(s):**
Hughes-Hallett, Deborah, et al. *Applied & Single Variable Calculus for Loyola University Chicago, Custom* (WileyPlus eBook).

**Prerequisites:**
MATH 131 or MATH 161

**Course description:**
A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, power series. This course is not a substitute for MATH 162.

**Syllabus:**
Common

## MATH 161. Calculus I

**Instructor(s):**
Staff

**Required text(s):**
Dwyer and Gruenwald. *Calculus: Resequenced for Students in Stem* (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

**Prerequisites:**
MATH 118

**Course description:**
A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, logarithmic and exponential functions. Applications to physics and other disciplines.

**Syllabus:**
Common

## MATH 162. Calculus II

**Instructor(s):**
Staff

**Required text(s):**
Dwyer and Gruenwald. *Calculus: Resequenced for Students in Stem* (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

**Prerequisites:**
MATH 161

**Course description:**
This course is a continuation of Calculus I and includes the calculus of various classes of functions, techniques of integration, applications of integral calculus, three-dimensional geometry, and differentiation and integration in two variables.

## MATH 201. Introduction to Discrete Mathematics & Number Theory (Section 01W)

**Instructor(s):**
Dr. Alan Saleski

**Required text(s):**
Hammack, The Book of Proof, 3rd edition
Also available for free on Hammack's website

**Prerequisites:**
MATH 161

**Course description:**
An introduction to writing clear and logical proofs. Topics to include naive set theory, combinatorics, first-order predicate logic, cardinality, relations, and functions.

**Syllabus:**
Biweekly quizzes, written homework, Midterm, and Final exam.
As this course is writing-intensive, two essays will be assigned.

## MATH 201. Introduction to Discrete Mathematics & Number Theory (Section 02W)

**Instructor(s):**
Dr. Carmen Rovi

**Required text(s):**
TBA

**Prerequisites:**
MATH 161

**Course description:**
This writing intensive course covers topics from discrete mathematics and number theory, areas of mathematics not seen in calculus courses and abundant in applications, and provides students with the concepts and techniques of mathematical proof needed in 300-level courses in mathematics. In particular, students will obtain an understanding of the basic concepts and techniques involved in constructing rigorous proofs of mathematical statements.

## MATH 212. Linear Algebra (Section 001)

**Instructor(s):**
Dr. Anthony Giaquinto

**Required text(s):**
Strang, Gilbert. *Linear Algebra for Everyone*. First Edition, Cambridge Wellesley Press, 2020, ISBN 978-1-7331466-3-0

**Prerequisites:**
MATH 132 or MATH 162

**Course description:**
Linear algebra is an indispensable tool in the sciences from pure mathematics to physics, engineering, computer science, data science, machine learning and imaging. This course will focus on the traditional topics of linear algebra including vector algebra and geometry, matrices, systems of linear equations, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors with an eye on applications and uses of these concepts. The new text selected for this course presents the material in an engaging way with the goal of "opening linear algebra to the world."

## MATH 212. Linear Algebra (Section 002)

**Instructor(s):**
Staff

**Required text(s):**
TBA

**Prerequisites:**
MATH 132 or MATH 162

**Course description:**
An introduction to linear algebra in abstract vector spaces with particular emphasis on R^n. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Software such as Mathematica may be utilized.

## MATH 263. Multivariate Calculus

**Instructor(s):**
Staff

**Required text(s):**
Dwyer and Gruenwald. *Calculus: Resequenced for Students in Stem* (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

**Prerequisites:**
MATH 162

**Course description:**
This course covers the differential and integral calculus of multivariable and vector valued functions, and sequences and infinite series, culminating with Green's Theorem, the Divergence Theorem, and Stokes' Theorem; software packages such as MAPLE may be used.

## MATH 263. Multivariate Calculus (A)

**Instructor(s):**
Dr. Brian Seguin

**Required text(s):**
Stewart, James. *Calculus: Early Transcendentals* (WebAssign eBook). 8th ed.

Print text (optional): ISBN-13: 978-1285741550. Boston: Cengage Learning, 2015.

**Prerequisites:**
MATH 162

**Course description:**
Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, LaGrange multipliers, multiple integrals, volume, surface area, the Change of Variables theorem, line integrals, surface integrals, Green's theorem, the Divergence Theorem, and Stokes' Theorem. Software packages such as MAPLE may be used. This course follows a traditional approach to calculus sequencing and is intended only for students with either AP credit or transfer credit equivalent to MATH 161 and MATH 162.

## MATH 264. Ordinary Differential Equations (Section 001)

**Instructor(s):**
Dr. Alla Podolny

**Required text(s):**
Elementary Differential Equations and Boundary Value Problems, 11th Edition, WILLIAM E. BOYCE, RICHARD C. DIPRIMA, DOUGLAS B. MEADE

**Prerequisites:**
MATH 263 or MATH 263 corequisite

**Course description:**
Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. They can describe exponential growth and decay, the population growth of species or the change in investment return over time.
This course will focus on ordinary differential equations.
We will start with building some basic mathematical models and classification of differential equations. Then we will proceed with exploring different types of first-order differential equations (both linear and nonlinear), second-order linear differential equations, systems of linear equations, numerical methods and we will finish this class investigating nonlinear differential equations and stability.
We will approach the concepts through a combination of analytic, graphic, and numeric methods. Some applications to modeling will be considered.
WileyPlus will be used for course resources and for online home works.
Grading will be based on home-works, weekly quizzes, midterms (tests/projects), and a cumulative final exam.
Please feel free to contact me at apodolny@luc.edu for more information.

## MATH 277. Problem Solving Seminar

**Instructor(s):**
Dr. Stephen London

**Required text(s):**
None

**Prerequisites:**
None

**Course description:**
In a seminar setting, students discuss and present proofs (or computer examples) as solutions to challenging and interesting problems including those from the Putnam and Virginia Tech mathematics competitions. Techniques are drawn from numerous areas of mathematics such as calculus of one and several variables, combinatorics, number theory, geometry, linear algebra, and abstract algebra.

## MATH 313. [ MATH 413 ] Abstract Algebra

**Instructor(s):**
Dr. Emily Peters

**Required text(s):**
Algebra: Abstract and Concrete, by Fred Goodman.
Abstract Algebra: Theory and Applications, by Thomas Judson

**Textbook notes:**
Both textbooks are available online for free:
Judson at
http://abstract.ups.edu/download.html
Goodman at
http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

**Prerequisites:**
MATH 201 and MATH 212

**Course description:**
Abstract algebra is, at heart, the study of symmetries. What do we mean when we say that a square is more symmetric than a (non-square) rectangle, or that a circle is more symmetric than a square? Which is more symmetric, a cube or an octahedron? The mathematical idea of a 'group' was created to make the idea of symmetry precise, and has taken on a vast life of its own, thanks to its broad applicability. Other examples of groups include: the numbers 0,...,n-1 in arithmetic modulo n; permutations of a group of identical objects; symmetries of the plane; symmetries of the plane that preserve distance (also known as isometries); symmetries of the plane that preserve area; and so forth.
This class will be example-driven but also rigorous and abstract. We will study equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.
Students will be assessed based on weekly homework, two midterms, a small number of quizzes, and class participation.

## MATH 315. [ MATH 415 ] Advanced Topics in Linear Algebra

**Instructor(s):**
Dr. Rafal Goebel

**Required text(s):**
Applied Linear Algebra by Olver and Shakiban,
2nd edition
Undegraduate Texts in Mathematics series, published by Springer
ISSN 0172-6056 or ISSN 2197-5604 (electronic),
ISBN 978-3-319-91040-6 or ISBN 978-3-319-910 41-3 (eBook)

**Prerequisites:**
Math 313

**Course description:**
Let's start with the first paragraph of the textbook:

Applied mathematics rests on two central pillars: calculus and linear algebra. While calculus has its roots in the universal laws of Newtonian physics, linear algebra arises from a much more mundane issue: the need to solve simple systems of linear algebraic equations. Despite its humble origins, linear algebra ends up playing a comparably profound role in both applied and theoretical mathematics, as well as in all of science and engineering, including computer science, data analysis and machine learning, imaging and signal processing, probability and statistics, economics, numerical analysis, mathematical biology, and many other disciplines. Nowadays, a proper grounding in both calculus and linear algebra is an essential prerequisite for a successful career in science, technology, engineering, statistics, data science, and, of course, mathematics.

This said, the course will build upon the students previous class on linear algebra, with focus on notions and techniques of linear algebra that are particularly relevant for applications, and will include select applications.

## MATH 331. [ COMP 331 COMP 431 MATH 431 ] Cryptography

**Instructor(s):**
Dr. Aaron Lauve

**Required text(s):**
TBA

**Recommended text(s):**
*Cryptography: An Introduction* (3rd Edition), by Nigel Smart. Self-published by the author at https://homes.esat.kuleuven.be/~nsmart/Crypto_Book/.

**Prerequisites:**
(COMP 163 or MATH 313 or MATH 201) and (COMP 125 or COMP 150 or COMP 170 or MATH/COMP 215).

**Course description:**
This interdisciplinary course treats the *mathematical* and *practical* theory of cryptographic systems. That is, the course will be a mixture of theory and practice, involving mathematical proofs, algorithm development (based on the mathematics), and coding—both in lectures and on homework assignments.

The course begins with a survey of historical systems (e.g., from Julius Caesar's time and *well before*), before spending some time on classical private-key (aka *symmetric*) systems, such as the Beaufort, Hill, Feistel, and Rijndael ciphers. Our main focus, however, will be public-key (*asymmetric*) cryptosystems, first appearing the 1970s, and now used *EVERYWHERE*—in every login to a secure website, in every credit card transaction, every time you ssh into a server to finish your MATH 331 homework, when companies store your password and personal data with hash functions, in Bitcoin, BitTorrent, as well as the modern sale of digital artwork.

We will develop the mathematics needed for Diffie-Hellman, RSA, and elliptic curve cryptography. The RSA algorithm is the gold-standard. *WARNING:* Quantum computers are coming! They will make RSA obsolete. We will soon need something new. Time permitting, we will also discuss the emerging theory of lattice-based cryptosystems.

Code demonstrations and assignments will be completed in Python 3. I have made arrangements for the necessary software to be installed on the campus computers; but students may wish to install on their machines as well. (This guide tells you what you need to do if you go the Anaconda route.)

**Syllabus:**
The course will involve biweekly quizzes and homework, one midterm exam, and a final exam.

## MATH 344. Geometry

**Instructor(s):**
Mr. Marius Radulescu

**Required text(s):**
Venema, Gerard. Foundations of Geometry. Pearson, 2012. ISBN-13: 978-0136020585

**Recommended text(s):**
Coxeter, H.S.M. and Greitzer, S.L. Geometry Revisited. Math Association of America, 1967. ISBN-13: 978-0883856192.
Greenberg. Euclidean and Non-Euclidean Geometries: Development and History, 3rd ed. W. H. Freeman, 2007. ISBN-13: 978-0716799481.

**Prerequisites:**
MATH 132 or 162. MATH 201 is recommended.

**Course description:**
This course is designed as an exploration of the traditional axiomatic treatment of geometry, including topics such as Euclid's Elements, axiomatic systems, the parallel postulates, neutral geometry, Euclidean geometry, hyperbolic geometry, constructions, transformations, and the classical models for non-Euclidean geometry.
The course is intended to give a deeper understanding of geometry and measurement with an emphasis on reasoning and presentation of mathematical ideas. We will use small group work to explore some of the unknown beautiful problems of classic geometry, revisit axiomatic systems and learn how to develop arguments based on logic.
Students will be graded based on homework, quizzes, a midterm exam and a final exam.

## MATH 351. [ MATH 451 ] Introduction to Real Analysis I

**Instructor(s):**
Dr. Tuyen Tran

**Required text(s):**
Introduction to Analysis, Maxwell Rosenlicht, Dover Books on Mathematics, ISBN 0-486-65038-3

**Prerequisites:**
Math 201, Math 212

**Course description:**
A rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: metric spaces, sequences and their convergence, continuity and differentiability of functions. After the course, students will be expected to formulate mathematical arguments and proofs. From time to time extra problems on homework/tests will be given for the students taking this class as MATH 451. These questions will count as extra credit for the students taking the class as MATH 351.

## MATH 353. [ MATH 488 ] Introduction to Complex Analysis

**Instructor(s):**
Dr. John Del Greco

**Required text(s):**
E. B. Saff and Snider, A. D., *Fundamentals of Complex Analysis with Applications to Engineering and Science*. 3rd ed. New Jersey: Pearson, 2003. Print.

**Prerequisites:**
Math 264

**Course description:**
In complex analysis we are interested in extending results using real numbers in algebra and analysis to analogous results using the field of complex numbers. Applications of this extension occur in electrical engineering, signal processing, quantum mechanics, and various mathematical fields such as number theory and real analysis.
Many concepts and results that seem non-intuitive when encountered in real analysis become “natural” when extended to their complex versions. We will study analytic functions, integration, infinite series, residue theory and conformal mappings.
Grading will be based on homework sets, three tests during the semester, and a final examination

## MATH 360. [ MATH 460 ] Game Theory

**Instructor(s):**
Dr. Peter Tingley

**Required text(s):**
Game Theory: An Introduction, Second Edition, by E. N. Barron, Wiley, 2013, ISBN 978-1-118-21693-4

**Prerequisites:**
MATH 162. Some 200 level math or stats is recommended.

**Course description:**
This is a mathematically rigorous introduction to the theory of games. Game theory is a branch of applied mathematics founded by John von Neumann with applications to economics, business, political science, optimization, differential equations, optimal transport, etc. It is the theory of finding optimal strategies in conflict or cooperative situations. It brings together most of undergraduate mathematics subjects to produce a subject which is important and fun to study.

**Syllabus:**
Two-person zero-sum games. Saddle points and mixed strategies. N-person non-zero sum games. Nash equilibria. Cooperative games with characteristic functions. Evolutionary population games.

## MATH 388. [ MATH 488 ] Differential Geometry of Curves and Surfaces

**Instructor(s):**
Dr. Brian Seguin

**Required text(s):**
There is no required text.

**Textbook notes:**
The instructor will provide pdfs and handwritten notes on the material throughout the semester.

**Prerequisites:**
MATH 263 and MATH 212

**Course description:**
This course is an introduction to differential geometry, focusing on curves and surfaces. Differential geometry studies the properties of curves, surfaces, and higher-dimensional curved spaces using tools from calculus and linear algebra. The use of calculus in geometry brings about paths of study for curved objects that extend beyond classical Euclidean geometry. Differential geometry contains some of the most beautiful results in mathematics and has applications to engineering and physics. For example, Einstein's general theory of relativity is impossible to do without tools from differential geometry. In particular, the concept of curvature, which we will discuss in this class in detail, plays an important role in relativity. The only pre-requisites for this course are good working knowledge of multivariable calculus and linear algebra.

## MATH 413. [ MATH 313 ] Abstract Algebra

**Instructor(s):**
Dr. Emily Peters

**Required text(s):**
Algebra: Abstract and Concrete, by Fred Goodman.
Abstract Algebra: Theory and Applications, by Thomas Judson

**Textbook notes:**
Both textbooks are available online for free:
Judson at
http://abstract.ups.edu/download.html
Goodman at
http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

**Prerequisites:**
MATH 201 and MATH 212

**Course description:**
Abstract algebra is, at heart, the study of symmetries. What do we mean when we say that a square is more symmetric than a (non-square) rectangle, or that a circle is more symmetric than a square? Which is more symmetric, a cube or an octahedron? The mathematical idea of a 'group' was created to make the idea of symmetry precise, and has taken on a vast life of its own, thanks to its broad applicability. Other examples of groups include: the numbers 0,...,n-1 in arithmetic modulo n; permutations of a group of identical objects; symmetries of the plane; symmetries of the plane that preserve distance (also known as isometries); symmetries of the plane that preserve area; and so forth.
This class will be example-driven but also rigorous and abstract. We will study equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.
Students will be assessed based on weekly homework, two midterms, a small number of quizzes, and class participation.

## MATH 415. [ MATH 315 ] Advanced Topics in Linear Algebra

**Instructor(s):**
Dr. Rafal Goebel

**Required text(s):**
Applied Linear Algebra by Olver and Shakiban,
2nd edition
Undegraduate Texts in Mathematics series, published by Springer
ISSN 0172-6056 or ISSN 2197-5604 (electronic),
ISBN 978-3-319-91040-6 or ISBN 978-3-319-910 41-3 (eBook)

**Prerequisites:**
Math 313

**Course description:**
Let's start with the first paragraph of the textbook:

Applied mathematics rests on two central pillars: calculus and linear algebra. While calculus has its roots in the universal laws of Newtonian physics, linear algebra arises from a much more mundane issue: the need to solve simple systems of linear algebraic equations. Despite its humble origins, linear algebra ends up playing a comparably profound role in both applied and theoretical mathematics, as well as in all of science and engineering, including computer science, data analysis and machine learning, imaging and signal processing, probability and statistics, economics, numerical analysis, mathematical biology, and many other disciplines. Nowadays, a proper grounding in both calculus and linear algebra is an essential prerequisite for a successful career in science, technology, engineering, statistics, data science, and, of course, mathematics.

This said, the course will build upon the students previous class on linear algebra, with focus on notions and techniques of linear algebra that are particularly relevant for applications, and will include select applications.

## MATH 431. [ COMP 331 COMP 431 MATH 331 ] Cryptography

**Instructor(s):**
Dr. Aaron Lauve

**Required text(s):**
TBA

**Recommended text(s):**
*Cryptography: An Introduction* (3rd Edition), by Nigel Smart. Self-published by the author at https://homes.esat.kuleuven.be/~nsmart/Crypto_Book/.

**Prerequisites:**
(COMP 163 or MATH 313 or MATH 201) and (COMP 125 or COMP 150 or COMP 170 or MATH/COMP 215).

**Course description:**
This interdisciplinary course treats the *mathematical* and *practical* theory of cryptographic systems. That is, the course will be a mixture of theory and practice, involving mathematical proofs, algorithm development (based on the mathematics), and coding—both in lectures and on homework assignments.

The course begins with a survey of historical systems (e.g., from Julius Caesar's time and *well before*), before spending some time on classical private-key (aka *symmetric*) systems, such as the Beaufort, Hill, Feistel, and Rijndael ciphers. Our main focus, however, will be public-key (*asymmetric*) cryptosystems, first appearing the 1970s, and now used *EVERYWHERE*—in every login to a secure website, in every credit card transaction, every time you ssh into a server to finish your MATH 331 homework, when companies store your password and personal data with hash functions, in Bitcoin, BitTorrent, as well as the modern sale of digital artwork.

We will develop the mathematics needed for Diffie-Hellman, RSA, and elliptic curve cryptography. The RSA algorithm is the gold-standard. *WARNING:* Quantum computers are coming! They will make RSA obsolete. We will soon need something new. Time permitting, we will also discuss the emerging theory of lattice-based cryptosystems.

Code demonstrations and assignments will be completed in Python 3. I have made arrangements for the necessary software to be installed on the campus computers; but students may wish to install on their machines as well. (This guide tells you what you need to do if you go the Anaconda route.)

**Syllabus:**
The course will involve biweekly quizzes and homework, one midterm exam, and a final exam.

## MATH 451. [ MATH 351 ] Introduction to Real Analysis I

**Instructor(s):**
Dr. Tuyen Tran

**Required text(s):**
Introduction to Analysis, Maxwell Rosenlicht, Dover Books on Mathematics, ISBN 0-486-65038-3

**Prerequisites:**
Math 201, Math 212

**Course description:**
A rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: metric spaces, sequences and their convergence, continuity and differentiability of functions. After the course, students will be expected to formulate mathematical arguments and proofs. From time to time extra problems on homework/tests will be given for the students taking this class as MATH 451. These questions will count as extra credit for the students taking the class as MATH 351.

## MATH 460. [ MATH 360 ] Game Theory

**Instructor(s):**
Dr. Peter Tingley

**Required text(s):**
Game Theory: An Introduction, Second Edition, by E. N. Barron, Wiley, 2013, ISBN 978-1-118-21693-4

**Prerequisites:**
MATH 162. Some 200 level math or stats is recommended.

**Course description:**
This is a mathematically rigorous introduction to the theory of games. Game theory is a branch of applied mathematics founded by John von Neumann with applications to economics, business, political science, optimization, differential equations, optimal transport, etc. It is the theory of finding optimal strategies in conflict or cooperative situations. It brings together most of undergraduate mathematics subjects to produce a subject which is important and fun to study.

**Syllabus:**
Two-person zero-sum games. Saddle points and mixed strategies. N-person non-zero sum games. Nash equilibria. Cooperative games with characteristic functions. Evolutionary population games.

## MATH 488. [ MATH 388 ] Differential Geometry of Curves and Surfaces

**Instructor(s):**
Dr. Brian Seguin

**Required text(s):**
There is no required text.

**Textbook notes:**
The instructor will provide pdfs and handwritten notes on the material throughout the semester.

**Prerequisites:**
MATH 263 and MATH 212

**Course description:**
This course is an introduction to differential geometry, focusing on curves and surfaces. Differential geometry studies the properties of curves, surfaces, and higher-dimensional curved spaces using tools from calculus and linear algebra. The use of calculus in geometry brings about paths of study for curved objects that extend beyond classical Euclidean geometry. Differential geometry contains some of the most beautiful results in mathematics and has applications to engineering and physics. For example, Einstein's general theory of relativity is impossible to do without tools from differential geometry. In particular, the concept of curvature, which we will discuss in this class in detail, plays an important role in relativity. The only pre-requisites for this course are good working knowledge of multivariable calculus and linear algebra.

## MATH 488. [ MATH 353 ] Introduction to Complex Analysis

**Instructor(s):**
Dr. John Del Greco

**Required text(s):**
E. B. Saff and Snider, A. D., *Fundamentals of Complex Analysis with Applications to Engineering and Science*. 3rd ed. New Jersey: Pearson, 2003. Print.

**Prerequisites:**
Math 264

**Course description:**
In complex analysis we are interested in extending results using real numbers in algebra and analysis to analogous results using the field of complex numbers. Applications of this extension occur in electrical engineering, signal processing, quantum mechanics, and various mathematical fields such as number theory and real analysis.
Many concepts and results that seem non-intuitive when encountered in real analysis become “natural” when extended to their complex versions. We will study analytic functions, integration, infinite series, residue theory and conformal mappings.
Grading will be based on homework sets, three tests during the semester, and a final examination

## STAT 103. Fundamentals of Statistics

**Instructor(s):**
Staff

**Required text(s):**
C.H. Brase and C.P. Brase. *Understanding Basic Statistics*, 7th ed (WebAssign eBook). Cengage.

**Prerequisites:**
None

**Course description:**
An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis.

**Syllabus:**
Common

## STAT 203. Statistics (Section 002)

**Instructor(s):**
Dr. Swarnali Banerjee

**Required text(s):**
Probability and Statistics for Engineering and the Sciences by Jay L. Devore.

**Recommended text(s):**
Essentials of Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye

**Prerequisites:**
MATH 162 or 132 (with grade of "C" or better).

**Course description:**
An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: experimental design, descriptive statistics, probability theory, sampling theory, inferential statistics, estimation theory, testing hypotheses, correlation theory, and regression.

## STAT 203. Statistics (Section 001)

**Instructor(s):**
Staff

**Required text(s):**
TBA

**Prerequisites:**
MATH 162 or 132 (with grade of "C" or better).

**Course description:**
An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: experimental design, descriptive statistics, probability theory, sampling theory, inferential statistics, estimation theory, testing hypotheses, correlation theory, and regression.

## STAT 307. [ STAT 407 ] Statistical Design and Analysis of Experiments

**Instructor(s):**
TBD

**Required text(s):**
TBD

**Prerequisites:**
STAT-308 or equivalent, or permission of the instructor.

**Course description:**
As no subject is more central to applied statistics and the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas.
Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. At the discretion of the instructor, grading is based on participation, homework assignments, a project/paper/presentation, exam(s) and a final.

## STAT 308. Applied Regression Analysis

**Instructor(s):**
Dr. Shuwen Lou

**Required text(s):**
Applied Regression Analysis and Other Multivariable Methods 5th Edition - Kleinbaum, Kupper, Nizam, Rosenberg. (Customized version for Loyola)

**Prerequisites:**
STAT 203 or STAT 335.

**Course description:**
Simple and multiple linear regression methods including weighted least squares and polynomial regression. Multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model. Use of packaged computer programs such as R.

## STAT 311. [ STAT 411 ] Applied Survival Analysis

**Instructor(s):**
Dr. Mike Perry

**Required text(s):**
Collett, David. Modelling Survival Data in Medical Research, 3rd. CRC Press, 2015.
ISBN: 978-1-4398-5678-9

**Recommended text(s):**
Allison, Paul D. Survival Analysis Using SAS: A Practical Guide 2nd, SAS Institute, 2010
Moore, Dirk, Applied Survival Analysis Usinr R, Springer
ISBN: 978-3-319-31243-9
ISBN (eBook): 978-3-319-31243-3

**Prerequisites:**
STAT 308 for those enrolled in STAT 311
None for those enrolled in STAT 411

**Course description:**
Time-to-event data, also referred to as survival data or failure-time data, arise in situations where the actual response measurements are not known, but are known to be below or above a threshold or within an interval. This course focuses on methods for analyzing such data.
We first consider descriptive methods for survival data including the survival function and its estimation using the Kaplan-Meier method and how to use and compare estimated survival functions. Then, we discuss several important regression models for survival data: semi-parametric models such as proportional hazards regression models and parametric models including exponential, Weibull and log-logistic regression models. Using ideas not unlike those used in linear regression models we will describe techniques for model development, including selecting covariates, identifying influential and poorly fit subjects, and assessing overall goodness-of-fit.
In this course, students will be required to analyze real-life data sets using R or SAS statistical packages.

**Syllabus:**
Grading:
Homework (Approximately 7) 15%
Exams (two at 20% each) 40%
Paper/Presentation 15%
Final Exam 30%

## STAT 321. [ COMP 356 STAT 421 ] Modeling & Simulation

**Instructor(s):**
Dr. Gregory J. Matthews

**Required text(s):**
Jones, O., Maillardet, R, and Robinson, A. *Introduction to Scientific Programming and Simulation Using R*. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6

**Prerequisites:**
STAT 308

**Course description:**
This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.

## STAT 335. Introduction to Biostatistics

**Instructor(s):**
Staff

**Required text(s):**
Varies - please consult individual instructor's syllabus.

**Prerequisites:**
MATH 162 or 132; BIOL 102

**Course description:**
An introduction to statistical methods used in data analysis. Topics include descriptive statistics, probability and sampling distribution, design of biological experiments, hypothesis testing, analysis of variance, and regression and correlation. Additionally, the course may include programming in R and analyzing R output.
(Note: Students may not receive credit for both STAT 203 & 335.)

## STAT 336. Advanced Biostatistics

**Instructor(s):**
Mr. Bret A Longman

**Required text(s):**
No required textbook

**Prerequisites:**
STAT 335

**Course description:**
This course covers multi-variate analysis, including advanced ANOVA, linear regression, logistic regression and survival analysis. The emphasis of the course is on applications instead of statistical theory, and students are required to analyze real-life datasets using the Minitab, SAS and/or R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, exams and a final.

## STAT 338. [ STAT 488 ] Predictive Analytics

**Instructor(s):**
Dr. Gregory J. Matthews

**Required text(s):**
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning, with Applications in R, (corrected 6th printing), Springer. ISBN/10: 1461471370, ISBN/13: 978-1461471370.

**Recommended text(s):**
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, (corrected 10th printing), Springer. ISBN-13: 978-0387848570 ISBN-10: 0387848576.

**Textbook notes:**
Note that an electronic copy of the required text is freely available for download at: http://www-bcf.usc.edu/ ∼gareth/ISL/
and the recommended text at http://statweb.stanford.edu/ ∼tibs/ElemStatLearn/

**Prerequisites:**
Some background in basic statistical methods or biostatistics including chi-square, ANOVA and simple regression, and maturity to get through somewhat sophisticated material. (STAT 308 or STAT 408 recommended)

**Course description:**
This course will cover a variety of statistical and machine learning techniques used to to predict and forecast future events. This will include supervised and unsupervised learning methods including potentially linear regression and classification, naive Bayes classifiers, cross-validation concepts, EM algorithm, generalized additive models (GAMS), tree based methods, boosting, neural networks, support vector machines, clustering, and random forests.

## STAT 370. Data Science Consulting

**Instructor(s):**
Dr. Swarnali Banerjee

**Required text(s):**
Cabrera,J. and McDougall, A. Statistical Consulting, Chapman & Hall.

**Prerequisites:**
STAT 308

**Course description:**
Students will be placed into groups of 3-5 students and assigned a
client to work with for the duration of the semester. Each group will provide regular
updates on the progress of the project via an oral presentation approximately every few
weeks. Additionally, at the end of the semester each group will submit a well-written
report documenting the problem, the data, the work they did, and future idea for new
directions. In addition to this group project, each student will be required to present on
topics previously chosen (needs approval). Presentations must be accompanied by well
written, informative slides. Student will also be graded based on their participation
during class. This includes, but is not limited to, asking relevant questions during the
group and individual presentations.

## STAT 396. Actuarial Seminar I

**Instructor(s):**
TBD

**Required text(s):**
TBD

**Prerequisites:**
MATH 263, MATH 212, MATH/STAT 304 are strongly recommended

**Course description:**
This seminar is for students who want to prepare for Society of Actuaries exam P, or (CAS Exam 1), Probability. Topics include general probability including conditional probability and Bayes rule, univariate distributions, including binomial, hypergeometric, Poisson, beta, Pareto, gamma, Weibull and normal, and multivariate distributions including joint moment generating functions and transformation techniques. May be repeated for credit.

## STAT 403. SAS Programming and Applied Statistics

**Instructor(s):**
Dr. Mike Perry

**Required text(s):**
None

**Recommended text(s):**
Cody, Ron P. and Jeffrey K. Smith, Applied Statistics and the SAS Programming Language, 5th ed., Pearson, 2006 ISBN-13: 978-0131465329

**Prerequisites:**
None

**Course description:**
Course Description: This course is an introduction to writing and executing SAS programs under the Windows environment in the context of applied statistics problems. SAS procedures are used to read and analyze various types of data sets as they apply to t-tests, simple and multiple regressions, ANOVA, categorical analysis, and repeated measures.

**Syllabus:**
Grading:
Approximately 7 homework assignments - 25%
4 quizzes - 20%
1 Take Home Test - 30%
1 Project and Presentation (2 papers and one slide presentation) - 25%

## STAT 407. [ STAT 307 ] Statistical Design and Analysis of Experiments

**Instructor(s):**
TBD

**Required text(s):**
TBD

**Prerequisites:**
STAT-308 or equivalent, or permission of the instructor.

**Course description:**
As no subject is more central to applied statistics and the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas.
Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. At the discretion of the instructor, grading is based on participation, homework assignments, a project/paper/presentation, exam(s) and a final.

## STAT 408. Applied Regression Analysis

**Instructor(s):**
TBD

**Required text(s):**
TBD

**Prerequisites:**
A basic statistical methods class (such as STAT-203 or 335 or equivalent)

**Course description:**
This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicolinearity will be discussed, as will be nonlinear and generalized linear regression. Coding will be introduced using the statistical software R. The course will focus on applications of linear regression as a tool for the analysis of real, possibly messy, data.

## STAT 411. [ STAT 311 ] Applied Survival Analysis

**Instructor(s):**
Dr. Mike Perry

**Required text(s):**
Collett, David. Modelling Survival Data in Medical Research, 3rd. CRC Press, 2015.
ISBN: 978-1-4398-5678-9

**Recommended text(s):**
Allison, Paul D. Survival Analysis Using SAS: A Practical Guide 2nd, SAS Institute, 2010
Moore, Dirk, Applied Survival Analysis Usinr R, Springer
ISBN: 978-3-319-31243-9
ISBN (eBook): 978-3-319-31243-3

**Prerequisites:**
STAT 308 for those enrolled in STAT 311
None for those enrolled in STAT 411

**Course description:**
Time-to-event data, also referred to as survival data or failure-time data, arise in situations where the actual response measurements are not known, but are known to be below or above a threshold or within an interval. This course focuses on methods for analyzing such data.
We first consider descriptive methods for survival data including the survival function and its estimation using the Kaplan-Meier method and how to use and compare estimated survival functions. Then, we discuss several important regression models for survival data: semi-parametric models such as proportional hazards regression models and parametric models including exponential, Weibull and log-logistic regression models. Using ideas not unlike those used in linear regression models we will describe techniques for model development, including selecting covariates, identifying influential and poorly fit subjects, and assessing overall goodness-of-fit.
In this course, students will be required to analyze real-life data sets using R or SAS statistical packages.

**Syllabus:**
Grading:
Homework (Approximately 7) 15%
Exams (two at 20% each) 40%
Paper/Presentation 15%
Final Exam 30%

## STAT 421. [ COMP 356 STAT 321 ] Modeling & Simulation

**Instructor(s):**
Dr. Gregory J. Matthews

**Required text(s):**
Jones, O., Maillardet, R, and Robinson, A. *Introduction to Scientific Programming and Simulation Using R*. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6

**Prerequisites:**
STAT 308

**Course description:**
This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.

## STAT 488. [ STAT 338 ] Predictive Analytics

**Instructor(s):**
Dr. Gregory J. Matthews

**Required text(s):**
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning, with Applications in R, (corrected 6th printing), Springer. ISBN/10: 1461471370, ISBN/13: 978-1461471370.

**Recommended text(s):**
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, (corrected 10th printing), Springer. ISBN-13: 978-0387848570 ISBN-10: 0387848576.

**Textbook notes:**
Note that an electronic copy of the required text is freely available for download at: http://www-bcf.usc.edu/ ∼gareth/ISL/
and the recommended text at http://statweb.stanford.edu/ ∼tibs/ElemStatLearn/

**Prerequisites:**
Some background in basic statistical methods or biostatistics including chi-square, ANOVA and simple regression, and maturity to get through somewhat sophisticated material. (STAT 308 or STAT 408 recommended)

**Course description:**
This course will cover a variety of statistical and machine learning techniques used to to predict and forecast future events. This will include supervised and unsupervised learning methods including potentially linear regression and classification, naive Bayes classifiers, cross-validation concepts, EM algorithm, generalized additive models (GAMS), tree based methods, boosting, neural networks, support vector machines, clustering, and random forests.

## STAT 488. Statistical Consulting

**Instructor(s):**
Dr. Swarnali Banerjee

**Required text(s):**
Cabrera,J. and McDougall, A. Statistical Consulting, Chapman & Hall.

**Prerequisites:**
Stat 404/405 and Stat 408 or permission of instructor.

**Course description:**
Students will be placed into groups of 3-5 students and assigned a
client to work with for the duration of the semester. Each group will provide regular
updates on the progress of the project via an oral presentation approximately every few
weeks. Additionally, at the end of the semester each group will submit a well-written
report documenting the problem, the data, the work they did, and future idea for new
directions. In addition to this group project, each student will be required to present
topics previously chosen (needs approval). Presentations must be accompanied by well
written, informative slides. Student will also be graded based on their participation
during class. This includes, but is not limited to, asking relevant questions during the
group and individual presentations.