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

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. 10th ed. ISBN-13: 978-1464124730. New York: W. H. Freeman, 2015. 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

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. 10th ed. ISBN-13: 978-1464124730. New York: W. H. Freeman, 2015. 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

Instructor(s):  Staff

Required text(s):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 6th ed.

Prerequisites:  Math 100 or Math Diagnostic Test

Course description:  The study of functions, their graphs, and their basic properties. Emphasis is placed on polynomial functions, including linear and quadratic functions. Study of polynomials includes zeros, factor theorem, and graphs. Additional topics include rational functions, transformations of functions, function composition and inverse functions.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 6th ed.

Prerequisites:  MATH 117 or Math Diagnostic Test

Course description:  A continuation of MATH 117 focusing on exponential, logarithmic, trigonometric, and inverse trigonometric functions, their graphs, and their properties. Techniques for solving equalities involving these functions are examined. Trigonometric identities, sum and difference formulas, double and half-angle formulas, the Laws of Sines and Cosines, and polar coordinates are also considered.

Syllabus:  Common

Instructor(s):  Mr. Marius Radulescu

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

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

Prerequisites:  None

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 focuses on problem solving on assigned topics. Students’ academic performance will be assessed based on homework and five quizzes. There is no final exam for this class.

Instructor(s):  Mr. Marius Radulescu

Required text(s):  None

Recommended text(s):  Sullivan, Michael. Precalculus. 11th ed., Pearson, 2020. ISBN-13 : 9780136845881

Prerequisites:  MATH 100 with a grade of A or A-

Course description:  A corequisite course that provides a rigorous transition from MATH 100 to MATH 118 for students whose high level of proficiency in advanced algebra recommends them for an accelerated path toward transcendental functions and trigonometry. The course will provide students with corequisite support and enrichment for the duration of the target course MATH 118. There are two main objectives of this course: to enrich students’ knowledge pertaining to topics from MATH 117, such as functions transformations and polynomials, through applications and problem-solving strategies, and to offer concurrent support for concepts and skills met along the way in MATH 118 that refer to content covered in MATH 117, such as rate of change, composition of functions and inverse functions. Students’ academic performance will be assessed based on homework and quizzes.

Instructor(s):  Laurie Jordan

Required text(s):  Brown, Peter, Roediger, Henry, McDaniel, Mark, "Make it stick"

Recommended text(s):  Su, Francis, "Mathematics for Human Flourishing" Firbhai-Illich Fatima, "Culturally Responsive Pedagogy"

Prerequisites:  MATH 131

Course description:  Students will learn best practices to communicate mathematical concepts and skills to diverse populations. The students will have an opportunity to engage in tutoring mathematics to the undergraduate population at Loyola. This course is designed to promote and encourage engagement and rigor in mathematical concepts and skills among the diverse communities of learners at Loyola. Students will be required to engage in approximately 20 hours of tutoring during the semester. The students will keep a log of the days and times that are devoted to tutoring and will be approved by the Lead Tutor/Supervisor of the Tutoring session. The Loyola Math Club will help facilitate the tutoring for all students in the Loyola undergraduate population. Currently the Loyola Math Club offers tutoring on Monday and Thursday nights from 7-9 pm for all Loyola undergraduates in 100-level Mathematics and Statistics courses. All undergraduate students are welcome to attend the tutoring on a drop-in basis. They may attend the tutoring as many times as they wish and for as long a session as they need to get their questions answered. The Club reserves a room in the STEM center to provide the in-person tutoring but has been tutoring remotely using Zoom.

Syllabus:  Math 123 E –Service Learning in Mathematics Spring Semester 2022L Loyola University Chicago Lake Shore Campus Section: 03E MWF 9:20-10:10 am Final: Saturday, May 7th, 2022 Instructor: Dr. Laurie Jordan Partnership Directors: Mohammed Abdul Mugsith mabdulmugsith@luc.edu Phone: 630-640-8401 cell Email: lbraga@luc.edu lauri1676@sbcglobal.net lj30w070@gmail.com Office Hours: By appointment via Zoom 11:30 – 12:20 MW in BVM 614 Diversity, Equity and Inclusion Statement: It is my intent to invest in each students’ success and that students from all diverse backgrounds and perspectives be well-served by this course, that students’ learning needs be addressed both in and out of class, and that the diversity that the students bring to this class be viewed as a resource, strength, and benefit. It is my intent to present materials and activities that are respectful of diversity, equity, and inclusion. Credit hours: 3 Prerequisites: Math 117 Course Description: Students will learn best practices to communicate mathematical concepts and skills to diverse populations. The students will have an opportunity to engage in tutoring mathematics to the undergraduate population at Loyola. This course is designed to promote and encourage engagement and rigor in mathematical concepts and skills among the diverse communities of learners at Loyola. Students will be required to engage in approximately 20 hours of tutoring during the semester. The students will keep a log of the days and times that are devoted to tutoring and will be approved by the Lead Tutor/Supervisor of the Tutoring session. The Loyola Math Club will help facilitate the tutoring for all students in the Loyola undergraduate population. Currently the Loyola Math Club offers tutoring on Monday and Thursday nights from 7-9 pm for all Loyola undergraduates in 100-level Mathematics and Statistics courses. All undergraduate students are welcome to attend the tutoring on a drop-in basis. They may attend the tutoring as many times as they wish and for as long a session as they need to get their questions answered. The Club reserves a room in the STEM center to provide the in-person tutoring but has been tutoring remotely using Zoom. MOST IMPORTANT TASK OF THIS COURSE: Recording your service hours: https://www.luc.edu/experiential/service-learning/howdoiserve/ https://www.luc.edu/media/lucedu/experiential/pdfs/LOCUS%20Tutorial08.15.17.pdf Course Outcomes: Students in this course will deepen their understanding of mathematical concepts and skills and be able to communicate this effectively to diverse communities of learners. Texts: Brown, P., Roediger III, H., & McDaniel, M. (2014). make it stick: The Science of Successful Learning. Cambridge: The Belknap Press of Harvard University Press. Fatima Pirbhai-Illich, S. P. (2017). Cultrually Responsive Pedagogy. Cham, Switzerland: Springer International Publishing. Su, F. (2020). Mathematics for Human Flourshing. New Haven: Yale University Press. Access to current textbooks used for courses in 100-level mathematics and statistics courses will be provided Syllabus Mathematical Focus Learning objective with relationship to mathematics and tutoring(2b) Intermediate Algebra (Math 100) Culturally responsive teaching Intermediate Algebra Learning retrieval tasks Precalculus I (Math 117) Power of retrieval Precalculus I Designing math retrieval tasks Precalculus II (Math 118) Assessing content Precalculus II Desirable difficulties Calculus I (Math 131) Extending learning Calculus I Art of reflection Calculus II Math (132) Perseverance in the face of failure Calculus II Generative Learning Calculus (Math 161) Encoding, consolidating and retrieval techniques Fundamentals of Statistics (STAT 103) Learning Style, Learning tips Modeling in the Real World (Math 108) Growth Mindsets in Mathematics, Technology bias Students will use each best practice skill to focus on a level of mathematics each week. Although every best practice can be applied to all levels of mathematics, each math course will be used to provide examples and practice each week. Students will be assessed on how well they can apply course content. Assessments may be (but are not limited to) reflections, role play in class, sample lesson demonstrations, use of questioning techniques or designing learning retrieval tasks. Assignments: Critical Reflections: Students in the course will be expected to keep journals of their tutoring sessions. Included in the journal will be what went well in the session, what could be improved, what are the obstacles and what are the goals for the next session. (Due weekly) These critical reflections should consider the following prompts: How well did I communicate with the students I tutored this week? How well did I determine what gaps in content knowledge were holding students back from being successful in their tests, quizzes and homework? Week 1 Assessment: Choose one student that you have worked with over the last week, how did you communicate with them? Did you provide examples from their background? What were the examples? How were the examples received? Week 2 Assessment: What learning retrieval tasks did you use with your students? Explain How did you determine if the tasks were effective? Week 3 Assessment: What tasks did you use to help students retrieve knowledge from previous courses? Explain how you did this? Week 4 Assessment: What math retrieval tasks did you design for quadratic equations? Week 5 Assessment: How were you able to diagnose where the student’s problem was? Was it reading the problem? Was it lack of sufficient background? Was it arithmetic skills? Was it Algebra skills? How did you determine how to help the student? Was your method successful? Week 6 Assessment: How were you able to provide appropriate challenges to the students you were tutoring while still respecting them? Week 7 Assessment: How were you able to extend the student’s learning from what they already knew to what they needed to know to be successful in the course that week? Week 8 Assessment: Please reflect on the experience of tutoring to date. How have your methods and views of tutoring changed? Week 9 Assessment: What methods have you used to preserve in tutoring Math 100 students? Did your methods work effectively for all the students that you tutored or just some? Why? Week 10 Assessment: How were you able to have the student generate their own learning? How did you effectively encourage students to own the material they were learning? Week 11 Assessment: What techniques have you learned that are most effective in dealing with underrepresented populations? Week 12 Assessment: What advice on learning style and learning tips would you give to other tutors? Learning objectives: Each learning objective will require an example of how it was applied to a tutoring session and a reflection on what happened and how it could be handled better. (Due after discussion of each learning objective)(4b) Culminating Experience/ Final 100 points : 3-Tiered Approach for Engaged Learning Assessment 2021-22 Students will respond to a standardized reflection prompt at the end of the semester, which Faculty will incorporate into their syllabi. Please note the student reflection instructions are here and tell students to scroll down to DIGICATION ENGAGED LEARNING STUDENT REFLECTION ASSESSMENT GUIDE. Please note this is a two-step process, as first students will self-enroll in the assessment group in Digication and then they will submit their reflection into the Engaged Learning category (academic internship, service-learning, etc.). Detailed instructions are on the link provided above. Instruct students to upload their reflection assignment into Digication. Students may find instructions on how to submit the assignment here and scroll down to DIGICATION ENGAGED LEARNING STUDENT REFLECTION ASSESSMENT GUIDE Please explain that this reflection must be completed by the end of the semester, after the students’ Engaged Learning experience in the course. This reflection prompt is intended to be one part of the ongoing reflection activities that instructors embed in their courses. Please encourage students to be detailed and provide examples to support their points in their reflection responses. The standardized reflection prompt is: “We are Chicago's Jesuit Catholic university- a diverse community seeking God in all things and working to expand knowledge in the service of humanity through learning, justice, and faith.” In an effort to assess the Engaged Learning University requirement, we ask all students enrolled in an Engaged Learning course to complete this reflection. Referencing Loyola’s mission statement above, compose a written reflection (at least 2 pages, double-spaced) that connects your in-class and out-of-class experience responding to the following: 1. How did you connect your in-class and out-of-class Engaged Learning experiences? 2. How did your Engaged Learning experience help you connect to the University’s mission? 3. How did the Engaged Learning experience in this course affect your personal, intellectual, civic, and/or professional development? Please submit your completed reflection in Digication, following instructions here. Grading: Completion of 20 hours of tutoring 200 points (approx. 10 points / hour) Completion of assessments 100 points Final 100 points Total 400 points Proposed Grading Scale: 400 - 368 A 367 – 356 B 355 – 285 C

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

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

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

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.

Syllabus:  Common

Instructor(s):  Dr. Stephen London

Required text(s):  Mathematics: A Discrete Introduction (3rd edition) by Edward Scheinerman ISBN-13: 978-0840065285 ISBN-10: 0840065280

Prerequisites:  MATH 161

Course description:  The course covers a variety of interesting topics from discrete mathematics including counting number theory, counting, cardinality, sets, and logic. These areas of mathematics have numerous applications in many fields of study. Central to the course is learning not just how to find an answer, but how to write solid mathematical arguments. Students will learn several proof writing techniques which will prepare them for upper level mathematics courses such as real and complex analysis and abstract algebra.

Syllabus:  Students will be given problem sets approximately regularly in addition to tests and a final.

Instructor(s):  Dr. Rafal Goebel

Required text(s):  Mathematics: A Discrete Introduction (3rd edition) by Edward Scheinerman ISBN-13: 978-0840065285 ISBN-10: 0840065280

Prerequisites:  MATH 161

Course description:  This writing-intensive course has two main goals: 1. Present a variety of topics in discrete math and in number theory. The topics range from prime numbers, studied already in ancient Greece, to graphs that can model friendships in a social network. The topics are also very different from what one sees in calculus, and so at the end of the course the student should have a more complete picture of what mathematics is about. 2. Teach the students how to read, formulate, and write rigorous mathematical arguments, including those known as proofs. This process begins with writing solutions to fairly basic problems, with complete explanations using proper English, and hopefully ends with the student being ready for upper-level math courses where proofs are unavoidable.

Instructor(s):  Dr. Peter Tingley

Required text(s):  .

Recommended text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. ISBN-13: 978-1118473504. New York: John Wiley, 2013. Print. Note: there is a 12th edition, but the 11th edition is cheaper, and I plan to follow that.

Textbook notes:  The text is very useful and a good reference, but I will also be providing a full set of lecture notes, and some people do not find the text is necessary. I highly recommend getting access to the text in some form though, since it contains many more examples and more detailed exposition than my notes.

Prerequisites:  MATH 132 or MATH 162

Course description:  This course will be a mathematically rigorous introduction to the basic concepts, theory, and applications of linear algebra. We will also spend significant time exploring the many wonderful applications of linear algebra to such fields as science, economics, business, engineering, computer science and the life sciences.

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.

Syllabus:  Common

Instructor(s):  Dr. Darius Wheeler

Required text(s):  Fundamentals of Differential Equations and Boundary Value Problems -- MyLab Math with Pearson eText, Digital Update ISBN-13: 9780137394494 | Published 2021

Prerequisites:  MATH 263 or MATH 263 corequisite

Course description:  Techniques for solving linear and non-linear first and second-order differential equations, the theory of linear second-order equations with constant coefficients, power series solutions of second-order equation, and topics in systems of linear first-order differential equations. Software such as MAPLE may be utilized.

Instructor(s):  Dr. Tuyen Tran

Required text(s):  Edwards, Penney and Calvis. Differential Equations and Linear Algebra, 4th edition. Published by Pearson. ISBN: 978-0134497181

Prerequisites:  MATH263

Course description:  The course is an introduction to linear algebra and differential equations, and is oriented toward students of engineering science. Topics include first and second-order differential equations, systems of first-order differential equations, systems of linear algebraic equations, matrix algebra, bases and dimension for vector spaces, linear independence, linear transformations, determinants, eigenvalues, and eigenvectors. Students will learn fundamental results and methods in ordinary differential equations and linear algebra.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  A first course in probablity. Sheldon Ross, Pearson Publishing, 10th edition, ISBN 978-0-13-475311-9.

Textbook notes:  9th edition is also OK, but exercise numbers might be different.

Prerequisites:  Math 263

Course description:  Probability is the mathematical study of chance. If you are interested in using math to describe anything that is not deterministic, you will need the tools of probability theory. Therefore, probability theory is foundational for many applied fields, including statistics and finance. This course will cover a discussion of probability, mean, and variance, independence, conditional probability, and random variables. We will consider both discrete probability spaces and probability spaces with continuously differentiable density functions. The course will include study of important probability distributions such as the binomial, exponential, Poisson, and normal distributions, the law of large numbers, and the central limit theorem. If time permits we will also consider Markov processes. Assessment in the course will consist of approximately weekly homework assignments, a few quizzes, two midterms, and a cumulative final exam.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 304

Course description:  In continuation of MATH/STAT 304, MATH/STAT 305 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Xiang Wan

Required text(s):  None.

Recommended text(s):  Numerical Analysis (10th ed) by Richard L. Burden, J. Douglas Faires, Annette M. Burden. Numerical Analysis (3rd ed) by Timothy Sauer (2018).

Prerequisites:  COMP 170 or MATH/COMP 215; (MATH 212 and MATH 264) or MATH 266

Course description:  Numerical Analysis (NA) is a subject on the theory and applications of numerical approximation of functions, derivatives, integrals, differential equations, etc. It is the sibling, as a discrete theory, of the continuous theory of such objects developed in Calculus and its sequels (including Math 264 ODE). The goals of NA are two-fold: (i) to develop algorithms that can be implemented by computers to realize these approximations; (ii) to theoretically establish the convergence, stability and error estimates of such developed algorithms.

Syllabus:  https://xiangwanmath.github.io/teaching

Instructor(s):  Dr. Emily Peters

Required text(s):  Algebra: Abstract and Concrete, by Frederick M. Goodman.

Textbook notes:  The textbook is no longer in print, but is available as a PDF from http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  Math 313

Course description:  Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Bogart, Kenneth, Combinatorics Through Guided Discovery, PreTeXt edition (2017), http://bogart.openmathbooks.org/.

Recommended text(s):  Keller, Mitchel T. and Trotter, William T.. Applied Combinatorics, PreTeXt edition (2017.2), https://www.rellek.net/book/.

Prerequisites:  MATH 162 or 162A

Course description:  We discover the joy and power of counting. (What a funny thing to say!) To some extent, the topics and techniques below show up in other domains of mathematics and computer science. So you could call this an applications course (indeed combinatorists at MIT are members of the "Applied Mathematics" department). But we'll mostly just be having fun, learning, all over again, how to count.

Topics: Basic counting techniques (e.g., additive principle, balls and boxes, binomial theorem); Distribution problems and other discrete structures (e.g., permutations, compositions, partitions, lattice paths, trees, Catalan numbers); proof techniques (e.g., pigeon-hole principle, induction, bijections); and advanced counting (e.g., inclusion-exclusion, generating functions). As time allows, additional topics may include: Eulerian walks, Hamiltionian cycles, electrical networks, posets, graph colorings, chromatic polynomials, Polya theory, combinatorial algorithms, Ramsey theory, and optimization, among others.

Syllabus:  Assessment: daily class prep; weekly homework (with some programming exercises); fortnightly quizzes; one midterm exam; and a final exam.

Graduate students will: complete more advanced exercises than the undergraduate students; help compile carefully worded definitions and theorems, with proofs; and will present some supplemental topics from independent reading.

Instructor(s):  Dr. Alan Saleski

Required text(s):  Arthur Mattuck, Introduction to Analysis (2013) (PDF also available)

Textbook notes:  Purchase the latest edition, otherwise, the problem numbers may not coincide.

Prerequisites:  Math 201, Intro to Number Theory and Discrete Mathematical Structures, Prentice-Hall (2013) Math 162: Intro to Calculus 2, including MV calculus

Course description:  TBA

Instructor(s):  Dr. Brian Seguin

Required text(s):  Rosenlicht, Maxwell. Introduction to Analysis Dover Publications, Inc. ISBN-10: 0-486-650383

Prerequisites:  MATH 351

Course description:  This course continues the careful derivation of the basic results first learned in calculus. We will cover most of what is in Chapters VI-X in the required book. This includes, but is not limited to, Riemann integration in R and R^n, derivatives in higher dimensions and partial derivatives, the implicit and inverse function theorems, and infinite series. The material for some of this topics will be taken from other sources and detailed lecture notes will be provided. The course will focus on the learning and understanding of concepts in analysis and the application of these concepts to prove results.

Instructor(s):  Dr. Christine Haught

Required text(s):  Michael Sipser, Introduction to the Theory of Computation, Cengage 2013. ISBN-13: 978-1-133-18779-0 ISBN-10: 1-133-18779-X, 3rd or 2nd edition

Prerequisites:  COMP 163 or MATH 201 or MATH 212.

Course description:  This is a course in the theory of computation. We will study what it means for a function or a set to be “computable”. In this study we will look at mathematical models of computation of increasing complexity – from simple pattern matching machines to the most complex modern computers and beyond. This field of study is important for computer science and mathematics students for a number of reasons. For practical reasons, understanding formal languages, grammars and models of computation gives valuable insight in pattern matching algorithms and programming languages. From a philosophical point of view, we will gain insight about the possibilities and limitations of computers and computation. We will use these models to prove and understand the Gödel Incompleteness Theorem (that any “reasonable” mathematical system for arithmetic contains true statements about numbers which cannot be proved). We will also study the time-space hierarchies within the computable universe. These hierarchies help us understand the differences between problems that can be solved quickly and efficiently and those that, while easy to state, may require astronomical time or space resources to solve. These notions are made precise in the classes P and NP, and understanding the famous question “Is P = NP?” There will be weekly homework assignments which will involve pencil and paper computation, calculations and writing rigorous arguments and proofs. Programming will be optional. There will be three in-class exams.

Instructor(s):  Dr. Carmen Rovi

Required text(s):  No text required

Prerequisites:  mostly intended for seniors, but juniors who have completed some upper-level math classes like 313 and/or 351 are also welcome.

Course description:  The Undergraduate Seminar in Mathematics will be a weekly, hour-long seminar where you will hear about some of the many deep and interesting areas of mathematics beyond what you would see in the classroom of most math classes. Students taking this class will be expected to give two brief lectures (one on a familiar topic from the curriculum, and one on a higher level material not customarily from the curriculum), and prepare an extended abstract summarizing the advanced material presented. The topics of student talks will be agreed upon with Dr. Rovi in advance and the students will receive guidance on the chosen topic and on how to give an effective presentation. Students will gain the ability to present material in Mathematics to a general audience. They will be graded based on their performance in presentations and abstracts, and on class participation.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 404

Course description:  In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Xiang Wan

Required text(s):  None.

Recommended text(s):  Numerical Analysis (10th ed) by Richard L. Burden, J. Douglas Faires, Annette M. Burden. Numerical Analysis (3rd ed) by Timothy Sauer (2018).

Prerequisites:  COMP 170 or MATH/COMP 215; (MATH 212 and MATH 264) or MATH 266

Course description:  Numerical Analysis (NA) is a subject on the theory and applications of numerical approximation of functions, derivatives, integrals, differential equations, etc. It is the sibling, as a discrete theory, of the continuous theory of such objects developed in Calculus and its sequels (including Math 264 ODE). The goals of NA are two-fold: (i) to develop algorithms that can be implemented by computers to realize these approximations; (ii) to theoretically establish the convergence, stability and error estimates of such developed algorithms.

Syllabus:  https://xiangwanmath.github.io/teaching

Instructor(s):  Dr. Emily Peters

Required text(s):  Algebra: Abstract and Concrete, by Frederick M. Goodman.

Textbook notes:  The textbook is no longer in print, but is available as a PDF from http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  Math 313

Course description:  Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Bogart, Kenneth, Combinatorics Through Guided Discovery, PreTeXt edition (2017), http://bogart.openmathbooks.org/.

Recommended text(s):  Keller, Mitchel T. and Trotter, William T.. Applied Combinatorics, PreTeXt edition (2017.2), https://www.rellek.net/book/.

Prerequisites:  MATH 162 or 162A

Course description:  We discover the joy and power of counting. (What a funny thing to say!) To some extent, the topics and techniques below show up in other domains of mathematics and computer science. So you could call this an applications course (indeed combinatorists at MIT are members of the "Applied Mathematics" department). But we'll mostly just be having fun, learning, all over again, how to count.

Topics: Basic counting techniques (e.g., additive principle, balls and boxes, binomial theorem); Distribution problems and other discrete structures (e.g., permutations, compositions, partitions, lattice paths, trees, Catalan numbers); proof techniques (e.g., pigeon-hole principle, induction, bijections); and advanced counting (e.g., inclusion-exclusion, generating functions). As time allows, additional topics may include: Eulerian walks, Hamiltionian cycles, electrical networks, posets, graph colorings, chromatic polynomials, Polya theory, combinatorial algorithms, Ramsey theory, and optimization, among others.

Syllabus:  Assessment: daily class prep; weekly homework (with some programming exercises); fortnightly quizzes; one midterm exam; and a final exam.

Graduate students will: complete more advanced exercises than the undergraduate students; help compile carefully worded definitions and theorems, with proofs; and will present some supplemental topics from independent reading.

Instructor(s):  Dr. Alan Saleski

Required text(s):  Arthur Mattuck, Introduction to Analysis (2013) (PDF also available)

Textbook notes:  Purchase the latest edition, otherwise, the problem numbers may not coincide.

Prerequisites:  Math 201, Intro to Number Theory and Discrete Mathematical Structures, Prentice-Hall (2013) Math 162: Intro to Calculus 2, including MV calculus

Course description:  TBA

Instructor(s):  Dr. Brian Seguin

Required text(s):  Rosenlicht, Maxwell. Introduction to Analysis Dover Publications, Inc. ISBN-10: 0-486-650383

Prerequisites:  MATH 351

Course description:  This course continues the careful derivation of the basic results first learned in calculus. We will cover most of what is in Chapters VI-X in the required book. This includes, but is not limited to, Riemann integration in R and R^n, derivatives in higher dimensions and partial derivatives, the implicit and inverse function theorems, and infinite series. The material for some of this topics will be taken from other sources and detailed lecture notes will be provided. The course will focus on the learning and understanding of concepts in analysis and the application of these concepts to prove results.

Instructor(s):  Dr. Christine Haught

Required text(s):  Michael Sipser, Introduction to the Theory of Computation, Cengage 2013. ISBN-13: 978-1-133-18779-0 ISBN-10: 1-133-18779-X, 3rd or 2nd edition

Prerequisites:  COMP 163 or MATH 201 or MATH 212.

Course description:  This is a course in the theory of computation. We will study what it means for a function or a set to be “computable”. In this study we will look at mathematical models of computation of increasing complexity – from simple pattern matching machines to the most complex modern computers and beyond. This field of study is important for computer science and mathematics students for a number of reasons. For practical reasons, understanding formal languages, grammars and models of computation gives valuable insight in pattern matching algorithms and programming languages. From a philosophical point of view, we will gain insight about the possibilities and limitations of computers and computation. We will use these models to prove and understand the Gödel Incompleteness Theorem (that any “reasonable” mathematical system for arithmetic contains true statements about numbers which cannot be proved). We will also study the time-space hierarchies within the computable universe. These hierarchies help us understand the differences between problems that can be solved quickly and efficiently and those that, while easy to state, may require astronomical time or space resources to solve. These notions are made precise in the classes P and NP, and understanding the famous question “Is P = NP?” There will be weekly homework assignments which will involve pencil and paper computation, calculations and writing rigorous arguments and proofs. Programming will be optional. There will be three in-class exams.

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.

Instructor(s):  Dr. Nan Miles Xi

Required text(s):  Probability and Statistics for Engineering and the Sciences 9th Edtion by Jay L. Devore.

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

Course description:  An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: Descriptive statistics, probability, random variables, probability distributions, random sample, point estimation, confidence interval, tests of hypotheses.

Instructor(s):  Dr. Mena Whalen

Required text(s):  Probability and Statistics for Engineering and the Sciences 9th Edtion by Jay L. Devore.

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

Course description:  An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: Descriptive statistics, probability, random variables, probability distributions, random sample, point estimation, confidence interval, tests of hypotheses

Instructor(s):  Dr. Shuwen Lou

Required text(s):  A first course in probablity. Sheldon Ross, Pearson Publishing, 10th edition, ISBN 978-0-13-475311-9.

Textbook notes:  9th edition is also OK, but exercise numbers might be different.

Prerequisites:  Math 263

Course description:  Probability is the mathematical study of chance. If you are interested in using math to describe anything that is not deterministic, you will need the tools of probability theory. Therefore, probability theory is foundational for many applied fields, including statistics and finance. This course will cover a discussion of probability, mean, and variance, independence, conditional probability, and random variables. We will consider both discrete probability spaces and probability spaces with continuously differentiable density functions. The course will include study of important probability distributions such as the binomial, exponential, Poisson, and normal distributions, the law of large numbers, and the central limit theorem. If time permits we will also consider Markov processes. Assessment in the course will consist of approximately weekly homework assignments, a few quizzes, two midterms, and a cumulative final exam.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 304

Course description:  In continuation of MATH/STAT 304, MATH/STAT 305 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  None

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, though no previous coding experience required. Evaluation will be made through take home exams as well as a semester long group project.

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  Either (STAT 203 or STAT 335) and Either (STAT 303 or STAT 308)

Course description:  An introduction to modern-day extensions of simple linear regression and ANOVA to the chi-square test including logistic regression and log-linear modelling techniques based on generalized linear models. Methods for matched-pair, small datasets, ordinal and multi-category data are also discussed. This course focuses on applications using real-life data sets, and uses popular software packages.

Instructor(s):  Dr. Timothy E. O'Brien

Required text(s):  M.L. Samuels, J.A. Witmer & A.A. Schaffner, Statistics for the Life Science, 5th edition (2016), Pearson: Boston, ISBN-13: 978-0-321-98958-1, ISBN-10: 0-321-98958-9

Prerequisites:  MATH 132 or 162; and BIOL 102

Course description:  This course provides an introduction to statistical methods used in designing biological experiments and analyzing biomedical, ecological and environmental data. Topics covered include basic probability (including prevalence, sensitivity and specificity assessment), frequency distributions, design of experiments, chi-square methods, interval estimation, tests of hypotheses, correlation and regression – all with a focus on biological and medical data. Time permitting, one-way ANOVA methods may be discussed. Students will be required to analyze real-life survival data using the R statistical (freeware) package. Assessment will be based on homework assignments, exams, and hands-on student projects.

Instructor(s):  Mrs. Sheila Suresh

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics, 8th edition, Cengage Publishing

Recommended text(s):  Samuels, Witmer, Schaffner. Statistics for the Life Sciences, 5th edition, Pearson Grant Publishing

Prerequisites:  BIOL 102, and MATH 132 or MATH 162. For Bioinformatics majors only: BIOL 101, and MATH 132 or MATH 162

Course description:  Introduction to Biostatistics is an introduction to statistical methods used in designing biological experiments and in data analysis. Topics include probability and sampling distribution, design of biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Additionally, the course will include computer laboratory assignments using R.

Instructor(s):  Dr. Izuchukwu Eze

Required text(s):  Samuels, Witmer, Schaffner. Statistics for the Life Sciences, 5th edition, Pearson Grant Publishing

Prerequisites:  BIOL 102, and MATH 132 or MATH 162. For Bioinformatics majors only: BIOL 101, and MATH 132 or MATH 162

Course description:  This course is an introduction to statistical methods used in designing biological experiments and analyzing biomedical, ecological and environmental data. Topics covered include basic probability, frequency distributions, design of experiments, chi-square methods, interval estimation, tests of hypotheses, correlation and regression – all with a focus on biological and medical data, and analysis of variance. Assessment will be based on homework assignments, exams, and final project. Additionally, the course will include computer laboratory assignments using R.

Instructor(s):  Mr. Bret A Longman

Required text(s):  None

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.

Instructor(s):  Dr. Nan Miles Xi

Required text(s):  There is no required textbook. The lecture notes will be posted on Sakai.

Recommended text(s):  Introduction to Bioinformatics with R: A Practical Guide for Biologists (2020). Edward Curry. CRC Press. Statistical Modeling and Machine Learning for Molecular Biology (2016). Alan Moses. CRC Press. An Introduction to Statistical Learning with Applications in R. Second Edition (2021). Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. Springer.

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  Introduction to statistical and machine learning methods in computational biology and bioinformatics. Emphasize understanding basic statistical and machine learning concepts and the ability to use those tools to solve biological problems. The tentative topics include: review of introductory probability and statistics, introduction to R programming language, statistical inference, multiple testing, clustering, dimension reduction, measure of association, linear regression, classification, resampling.

Instructor(s):  Dr. Michael Perry

Required text(s):  None

Recommended text(s):  Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. Wiley. 2014 (Note, you can find a pdf version online) Higgins, James J. "Introduction to Modern Nonparametric Statistics." Brooks/Cole. 2004

Prerequisites:  STAT 203 or STAT 335

Course description:  This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression. R programming language will be used to perform many of the techniques and analysis. Students should be familiar with this language.

Syllabus:  Grade calculation Midterm Exam: 25% Final Exam: 30% Homework: 30% Project 15%

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 404

Course description:  In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  Either (STAT 203 or STAT 335) and Either (STAT 303 or STAT 308)

Course description:  An introduction to modern-day extensions of simple linear regression and ANOVA to the chi-square test including logistic regression and log-linear modelling techniques based on generalized linear models. Methods for matched-pair, small datasets, ordinal and multi-category data are also discussed. This course focuses on applications using real-life data sets, and uses popular software packages.

Instructor(s):  Dr. Nan Miles Xi

Required text(s):  There is no required textbook. The lecture notes will be posted on Sakai.

Recommended text(s):  Introduction to Bioinformatics with R: A Practical Guide for Biologists (2020). Edward Curry. CRC Press. Statistical Modeling and Machine Learning for Molecular Biology (2016). Alan Moses. CRC Press. An Introduction to Statistical Learning with Applications in R. Second Edition (2021). Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. Springer.

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  Introduction to statistical and machine learning methods in computational biology and bioinformatics. Emphasize understanding basic statistical and machine learning concepts and the ability to use those tools to solve biological problems. The tentative topics include: review of introductory probability and statistics, introduction to R programming language, statistical inference, multiple testing, clustering, dimension reduction, measure of association, linear regression, classification, resampling.

Instructor(s):  Dr. Michael Perry

Required text(s):  None

Recommended text(s):  Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. Wiley. 2014 (Note, you can find a pdf version online) Higgins, James J. "Introduction to Modern Nonparametric Statistics." Brooks/Cole. 2004

Prerequisites:  STAT 203 or STAT 335

Course description:  This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression. R programming language will be used to perform many of the techniques and analysis. Students should be familiar with this language.

Syllabus:  Grade calculation Midterm Exam: 25% Final Exam: 30% Homework: 30% Project 15%