Department of Mathematics and Statistics, Binghamton University people:alex

Math 222 (Calculus 2) Fall 2015

2015-12-28T18:06:42-04:00

Syllabus for Math 222, Fall 2015

General Information About All Sections

Contact Information

The instructor for your section will provide you with contact information. General Administration of Course: Prof. Alex Feingold

Class Meeting Schedule - All Sections

Section	Instructor	Days	Times	Room
01	Binbin Huang	MWF	8:00-9:30	LN 2409
02	Simon Joyce	MWF	8:00-9:30	LN 2447
03	David Biddle	MWF	8:00-9:30	EB R15
04	Mathew Wolak	MWF	8:00-9:30	SL 302
05	Binbin Huang	MWF	9:40-11:10	LN 2409
06	Simon Joyce	MWF	9:40-11:10	LN 2447
07	Alex Feingold	MWF	9:40-11:10	WH G002
08	Jaiung Jun	MWF	11:20-12:50	LN 2409
09	Adam Allan	MWF	11:20-12:50	LN 2447
10	Matt Zaremsky	MWF	11:20-12:50	WH G002

Prerequisites

A grade of C- or better in Calculus I is required, but a grade of C or better is HIGHLY RECOMMENDED. Historical data shows that students with just C- in Calculus I usually had serious trouble in Calculus II. You have been warned!

Office Hours

Each instructor will inform you of office hours or scheduled problem sessions outside of class times.

Textbook

``Calculus Single Variable'' by James Stewart, Eighth Edition (with WebAssign Access Code), Cengage Learning, 20 Channel Center Street, Boston, MA 02210, USA, ISBN: 978-1-305-26663-6.

Objectives and Course Contents

The main goal of Calculus II is to continue the development of differential and integral calculus started in Calculus I, including specific topics which have been found to be valuable for applications in many other fields. Students will be introduced to new classes of functions including the exponential functions, logarithm functions, and inverse trig functions. Students will then learn how to apply the techniques of Calculus (differentiation and integration) to those functions. The method of L'Hospital's Rule will be taught for dealing with certain limits. Various techniques for integration will be taught (integration by parts, trig integrals, trig substitutions, partial fractions, and improper integrals). Infinite sequences and series will be studied, and methods for investigation of their convergence will be taught (the integral test, the comparison tests, the ratio and root tests, alternating series, absolute convergence and power series). Methods of representing functions as power series with a radius of convergence will be taught, as well as the Taylor series representations of a given function. We will study several applications of integration, including: finding the length of arc of a curve, finding the area of a surface of revolution (even when the equations are given in parametric form, in rectangular or polar coordinates). Depending on time, the course may conclude with the study of conic sections. The course material is vital to the study of Calculus III and Differential Equations, and is very useful in many other courses in the Department of Mathematical Sciences and in other departments (e.g., Physics, Chemistry, Biology, and Economics).

Help Outside of Class

The Calculus 2 Help Room room, located in Whitney Hall (WH-235), is staffed by some of the instructors and will be open starting Sept. 8, 2015, during most business hours. Students can walk in with no appointment and can ask questions of any available instructor. The exact schedule for this semester will be posted here soon. Click here for the Help Room schedule.

People learn in many different ways: through reading, listening, practicing and working with others. Students may wish to work with others while doing the practice problems or preparing for an exam. That is acceptable and even encouraged. However, unethical behavior in this class will not be tolerated. Cheating on an examination, or any other ethics violation, will result in a serious penalty. See the section below on Academic Honesty.

General Comments

Regular class attendance is required for success in this course. Lack of attendance will most likely result in a lower grade. When a student does not come to class, it is a clear message to the instructor that the student does not think he/she can teach them. The instructor may assign 30 points of your total score based on attendance, classroom participation or additional quizzes, and will decide borderline cases. The material is a combination of theory and calculation, and it is necessary to understand the theory in order to do sensible calculations and interpret them correctly. Lectures can be interrupted at any time for questions. At the start of each class be ready to ask questions about homework problems or about the previous lecture. A grade of C or better in Calculus I is strongly recommended for this course. If you do not meet that condition, see the instructor immediately for advice.

Student use of cell phones and other electronic devices is becoming increasingly disruptive in class and is actually insulting to the instructor. Holding the cell phone in your lap and looking down to text does not make you invisible! All electronics should be turned off and put away before the beginning of class. Students found using such devices may be asked to leave the class.

University Attendance Policy

Students are expected to attend all scheduled classes, laboratories and discussions. Instructors may establish their own attendance criteria for a course. They may establish both the number of absences permitted to receive credit for the course and the number of absences after which the final grade may be adjusted downward. In such cases it is expected that the instructor stipulate such requirements in the syllabus and that the syllabus be made available to students at or near the beginning of classes. In the absence of such statements, instructors have the right to deny a student the privilege of taking the final examination or of receiving credit for the course, or may prescribe other academic penalties if the student misses more than 25 percent of the total class sessions. Excessive tardiness may count as absence.

If you are seriously ill (running a fever, upset stomach) you should not come to class. Documented illness of this sort is an excused absence and will not be counted against your attendance grade. Absence for more than one or two days needs to be documented by health services. If you are going to be ill for an extended period of time (a week or more) be sure to contact your instructor as soon as you can so that plans can be made for you to make up the work you will be missing.

Homework

For each section of material covered there will be an assignment of problems on WebAssign. Your WebAssign homework counts towards your grade. Study groups are encouraged, but students should not become too dependent on others. Watching the instructor, or other students, do the problems will not be enough to learn the material. It will be necessary for you to do many exercises yourself in order to be successful on the exams. Attempts to solve homework problems provide the best way to learn the material and to prepare for exams.

WebAssign is an online homework system which includes an e-book version of our text. If you buy the textbook through the University bookstore it comes with an access code for WebAssign. If you do not buy the textbook from the bookstore then you will need to purchase an access code on the WebAssign website. You will have temporary free access to WebAssign for 2 weeks into the semester without an access code. If you bought a WebAssign access code from a previous semester, you do not have to buy it again. (Exception: if you only purchased one-semester access, you'll need to buy it again.) When logging into WebAssign for the first time you will need to self-enroll with a “Class Key”. The “Class Key” will be provided to you by your instructor. All info for getting started with WebAssign can be found here WebAssign Student Quick Start Guide

Your username is your Binghamton University username and the institution code is “binghamton”.

Exams, Grading and Cheating

There will be a total of 600 possible points, distributed in the following way:

WebAssign Homework	40 Points
Instructor Adjustments	30 Points
Quizzes	30 points (for example, ten 3-point quizzes)
Exam 1	100 points
Exam 2	100 points
Exam 3	100 points
Final Exam	200 points.

Instructor adjustments to your grade may include: additional quizzes, attendance and classroom participation. Your grade will be determined primarily by your numerical scores on the quizzes, WebAssign homework, three exams and the final exam. For each exam the numerical score will be given a letter grade interpretation in order to give you some idea of how you stand in relation to all other students in the course. Your Total of all points at the end of the course will also be given a letter grade interpretation, which should be consistent with the average of all previous letter grades. Borderline cases can be adjusted up or down based on your instructor's judgment.

Here is a link to a practice Exam 1 and its solutions.

Here is a link to This semester's Exam 1 Version 1 and its solutions.

Here is a link to This semester's Exam 1 Version 2 and its solutions.

Here are the letter grade interpretations of the numerical scores on Exam 1. The average over all sections was 81.63.

Letter Grade	Numerical Range
A	92 - 100
A-	88 - 91
B+	84 - 87
B	77 - 83
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	55 - 59
D	50 - 54
F	0 - 49

Here is a link to a practice Exam 2.

Here is a link to Solutions to that practice Exam 2.

Here is a link to This semester's Exam 2 Version 1 solutions.

Here is a link to This semester's Exam 2 Version 2 solutions.

Here are the letter grade interpretations of the numerical scores on Exam 2. The average over all sections was 73.38.

Letter Grade	Numerical Range
A	90 - 100
A-	86 - 89
B+	82 - 85
B	75 - 81
B-	70 - 74
C+	64 - 69
C	56 - 63
C-	50 - 55
D	41 - 49
F	0 - 40

Here is a link to a practice Exam 3.

Here is a link to Solutions to that practice Exam 3.

Here is a link to This semester's Exam 3 Version 1 solutions.

Here is a link to This semester's Exam 3 Version 2 solutions.

Here are the letter grade interpretations of the numerical scores on Exam 3. The average over all sections was 78.24.

Letter Grade	Numerical Range
A	92 - 100
A-	88 - 91
B+	83 - 87
B	77 - 82
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	54 - 59
D	46 - 53
F	0 - 45

Here is a link to practice final exam problems covering sections 10.1-10.4.

Here are the letter grade interpretations of the numerical scores on the Final Exam. The average over all sections was 138.

Letter Grade	Numerical Range
A	180 - 200
A-	170 - 179
B+	160 - 169
B	150 - 159
B-	140 - 149
C+	130 - 130
C	110 - 129
C-	95 - 109
D	80 - 94
F	0 - 49

Before each exam a practice exam will be posted here as a pdf file you may download. It will have the questions first, which you should try to answer without looking at the solutions. After each exam is graded and returned, a set of solutions will be posted here on this webpage. You should compare your exam to the solutions, and understand your mistakes so you will be able to do such problems correctly in the future. That would be a very good way to prepare for the final exam. If you do not understand your mistakes, or think your exam was not correctly graded, you should immediately (at most within two days) bring the test to your instructor for re-evaluation. If you are not satisfied with the re-evaluation of your test, you can appeal to the course coordinator, Prof. Feingold, whose decision will be final. DO NOT MAKE ANY CHANGES OR WRITE NEW MATERIAL ON YOUR GRADED EXAM!! Turning in a modified exam for extra points is CHEATING. Instructors may be making copies of random exams before they are returned, so if a student changes a graded exam, it will be clearly shown by comparison with the copy.

Any cases of cheating will be subject to investigation by the Academic Honesty Committee of Harpur College.

Academic Honesty

Cheating is considered a very serious offense. According to the University Catalog, cheating consists of: “Giving or receiving unauthorized help before, during or after an examination”. The full strength of Binghamton Academic Honesty Policy will be applied to anyone caught cheating. This may include failing the course, and further disciplinary action.

Administration of Exams

All exams for all sections will be administered at your normal meeting time in your normal meeting room.

The dates, times and places given below for Exams 1, 2 and 3 will be confirmed or modified before each exam.

The final exam for all sections will be administered in a common exam during Finals Week.

The schedule of exams is as follows:

Exam 1: Friday, Sept. 25, 2015.

Exam 2: Wednesday, Oct. 21, 2015.

Exam 3: Wednesday, December 2, 2015.

Final Exam: Thursday, Dec. 17, 2015, 5:40-7:40 PM, GW-69 (Gym West) for all sections.

Note that the Add/Drop Deadline is Sept. 11, 2015 , and the Withdrawal Deadline is Oct. 30, 2015.

A detailed content of each exam will be determined one week before the exam, but we expect it to be as follows:

Exam 1: Sec. 6.1, 6.2*, 6.3*, 6.4*, 6.5, 6.6, 6.8.

Exam 2: Sec. 7.1 - 7.4, 7.8, 11.1.

Exam 3: 11.2 - 11.11, 8.1, 8.2.

The Final Exam will be comprehensive, covering the whole course, including material covered from chapter 10.

Important Note: No use of calculators, cellphones or laptop computers will be allowed during exams.

Scientific calculators may be needed for some homework.

ANYONE UNABLE TO TAKE AN EXAM SHOULD CONTACT THEIR INSTRUCTOR AHEAD OF TIME TO EXPLAIN THE REASON. NO ONE SHOULD MISS THE FINAL UNLESS YOU HAVE A CONFLICT WITH ANOTHER FINAL EXAM. IF YOU HAVE SUCH A CONFLICT, YOU SHOULD TELL YOUR INSTRUCTOR ABOUT IT AT THE START OF THE SEMESTER.

Note: Some students may have class schedule conflicts with the evening exams. Arrangements will be made to accommodate these students so that they will not have to miss other classes. Notify your instructor immediately if you have a problem taking the scheduled evening exams. Conflicts other than class schedule conflicts will not be accommodated and therefore should be resolved by the student in a timely manner. Students who miss an exam because of illness must contact the instructor ahead of the exam (or as soon afterwards as possible) and provide proof of the illness (doctor's note or call from health service).

Schedule

Week 1: Aug. 31 - Sept. 4	6.1, 6.2, 6.3
Week 2: Sept. 7 - Sept. 11	6.4*, 6.5
Week 3: Sept. 14 - 18	6.6, 6.8
Week 4: Sept. 21 - 25	Review, Exam 1
Week 5: Sept. 28 - Oct. 2	7.1, 7.2, 7.3
Week 6: Oct. 5 - Oct. 9	7.4, 7.8
Week 7: Oct. 12 - 16	11.1, 11.2
Week 8: Oct. 19 - 23	Review, Exam 2, 11.2
Week 9: Oct. 26 - 30	11.3, 11.4
Week 10: Nov. 2 - 6	11.5, 11.6
Week 11: Nov. 9 - 13	11.8, 11.9
Week 12: Nov. 16 - 20	11.10, 11.11
Week 13: Nov. 23 - 27	8.1, 8.2
Week 14: Nov. 30 - Dec. 4	Review, Exam 3, 10.1
Week 15: Dec. 7 - 11	10.2, 10.3, 10.4
Week 16: Dec. 14 - 18	Review, Final Exam

Supplementary Materials and Links

Here we provide links to documents and websites you may find useful throughout the semester. They do not constitute an official part of the course, nor are they endorsed by the Department of Mathematical Sciences. Use them at your own discretion.

Factorization of polynomials (Useful for working with Partial Fractions)

Useful Limits to Know

Guide to Checking Convergence/Divergence of Series

The following are pdf files with a polar coordinates grid (in radians or degrees) on which you can conveniently make graphs of functions given in polar coordinates.

Polar Coordinates Graph (radians)

Polar Coordinates Graph (degrees)

Visual Calculus - Step by step tutorial on the topics of our course.

For Calc II see:

An excellent source for math videos

Another excellent source for math videos

Integration: Techniques of Integration, Numerical Integration, Improper Integrals

Sequences, Series, Power Series

Cycloid

Visual Calculus has guided tutorials on almost all the subjects we're doing. You see a question posted and work on it. If you click on the link, it will do one step of the solution. If that helps you, fine. If not, click again and it will show the next step. Thus, if you get stuck, you can get one hint at a time. It won't give away the answer all at once, so you can practice each step for yourself. Try it!

Calculus On the Web an online tutorial.

The math forum - various math resources. Check out the topics on calculus

MathWorld - more math resources.

Mathnerds - get hints on your math questions.

The archives - Copies of the Math 222 home page for previous semesters.

Math 222 (Calculus 2) Spring 2015

2015-12-28T18:07:21-04:00

Syllabus for Math 222, Spring 2015

General Information About All Sections

Contact Information

The instructor for your section will provide you with contact information. General Administration of Course: Prof. Alex Feingold

Class Meeting Schedule - All Sections

Section	Instructor	Days	Times	Room
01	Alex Feingold	MWF T	10:50-11:50 10:05-11:30	AP G14 LN G208
02	Diego Penta	MWF R	9:40-10:40 8:30-9:55	AP G15 LN G332
03	Withanage De Mel	MWF R	10:50-11:50 10:05-11:30	AP G15 LN G208
04	Gangotryi Sorcar	MWF R	12:00-1:00 11:40-1:05	AP G14 AP G15
05	Patrick Milano	MWF T	12:00-1:00 11:40-1:05	AP G15 AP G15
06	Elizabeth Perry	MWF T	1:10-2:10 10:05-11:30	AP G14 LN G209
07	Kevin Klonoff	MWF R	1:10-2:10 10:05-11:30	OR 100D LN G209
08	Walter Carlip	MWF T	2:20-3:20 4:25-5:50	FA 209 S2 144
09	Andrew Kelley	MWF R	2:20-3:20 4:25-5:50	OR 100D S2 143
10	David Biddle	MWF R	3:30-4:30 4:25-5:50	AP G15 S2 260
11	Qiyi Lu	MWF T	3:30-4:30 4:25-5:50	LN 2403 S2 260
12	Laura Anderson	MWF	8:00-9:30 SL 206
13	Simon Joyce	MWF	8:00-9:30	SL 210
14	Simon Joyce	MWF T	9:40-10:40 8:30-9:55	LN G335 LN G335
15	William Kazmierczak	MWF	8:00-9:30	SL 306

Prerequisites

Office Hours

Each instructor will inform you of office hours or scheduled problem sessions outside of class times.

Textbook

``Calculus Single Variable'' by James Stewart, 7E (with WebAssign Access Code), Brooks/Cole - Thomson Learning Publishing Company, Pine Grove, CA, 2008, ISBN-10: 0495011614.

Objectives and Course Contents

Help Outside of Class

The Calculus 2 Help Room room, located in Whitney Hall (WH-233), is staffed by some of the instructors and will be open starting Feb. 2, 2015, during most business hours. Students can walk in with no appointment and can ask questions of any available instructor. The exact schedule for this semester will be posted here soon. Click here for the Help Room schedule.

General Comments

University Attendance Policy

Homework

Your username is your Binghamton University username and the institution code is “binghamton”.

Exams, Grading and Cheating

There will be a total of 600 possible points, distributed in the following way:

WebAssign Homework	40 Points
Instructor Adjustments	30 Points
Quizzes	30 points (for example, ten 3-point quizzes)
Exam 1	100 points
Exam 2	100 points
Exam 3	100 points
Final Exam	200 points.

Here is a link to a practice Exam 1 and its solutions.

Here is a link to Exam 1 and its solutions.

Here is a table of letter grade interpretations of the numerical scores for Exam 1. The average on Exam 1 over all sections was about 81.

Letter Grade Interpretation	Score Range
A	92 - 100
A-	88 - 91
B+	84 - 87
B	77 - 83
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	55 - 59
D	50 - 54
F	0 - 49

Here is a link to a practice Exam 2.

Here is a link to Solutions to that practice Exam 2.

Here is a link to Exam 2 and its solutions.

A table of letter grade interpretations of the numerical scores for Exam 2 is below. The average on Exam 2 over all sections was about 67.

Letter Grade Interpretation	Score Range
A	90 - 100
A-	85 - 89
B+	80 - 84
B	75 - 79
B-	70 - 74
C+	65 - 69
C	55 - 64
C-	50 - 54
D	40 - 49
F	0 - 39

The following new version of practice Exam 3 has been adjusted on 4-1-2015 to match the material you will need to know for Exam 3 this semester. Check with your instructor for more details about what material is being skipped in each section, and what material you are responsible for on exams. This is not an April Fools Joke!

Here is a link to a practice Exam 3.

Here is a link to Solutions to that practice Exam 3.

Here is a link to Exam 3 solutions.

A table of letter grade interpretations of the numerical scores for Exam 3 is below. The average on Exam 3 over all sections was about 74.

Letter Grade Interpretation	Score Range
A	92 - 100
A-	88 - 91
B+	83 - 87
B	77 - 82
B-	72 - 76
C+	67 - 71
C	60 - 66
C-	52 - 59
D	45 - 51
F	0 - 44

Here is a link to practice final exam problems covering sections 10.1-10.4.

A table of letter grade interpretations of the numerical scores for the Final Exam is below. The average on the Final Exam over all sections was about 125.

Letter Grade Interpretation	Score Range
A	170 - 200
A-	160 - 169
B+	145 - 159
B	127 - 144
B-	116 - 126
C+	106 - 115
C	86 - 105
C-	78 - 85
D	65 - 77
F	0 - 64

A table of letter grade interpretations of the numerical scores for the Total Course Points is below. The average on the Total Course Points over all sections was about 418.

Letter Grade Interpretation	Score Range
A	520 - 600
A-	500 - 519
B+	470 - 499
B	420 - 469
B-	400 - 419
C+	360 - 399
C	320 - 359
C-	280 - 319
D	240 - 279
F	0 - 239

Any cases of cheating will be subject to investigation by the Academic Honesty Committee of Harpur College.

Academic Honesty

Administration of Exams

All exams for all sections will be administered at a common evening time between 7:00 and 9:00 PM, depending on your section.

The dates, times and places given below for Exams 1, 2 and 3 will be confirmed or modified before each exam.

The final exam for all sections will be administered in a common exam during Finals Week.

The class will be divided to fit in six rooms as follows (subject to adjustment):

Sections	Exam Room	Time
1 - 3	LH-2	7:00 - 8:30 PM
4 - 6	LH-8	7:00 - 8:30 PM
7 - 9	LH-14	7:00 - 8:30 PM
10 - 11	AA-G008	7:00 - 8:30 PM
12, 15	EB-110	7:30 - 9:00 PM
13, 14	S1-149	7:00 - 8:30 PM

NOTE: Sections 12 and 15 in EB-110 have a shifted time.

The schedule of exams is as follows:

Exam 1: Wednesday, Feb. 18, 2015.

Exam 2: Wednesday, Mar. 18, 2015.

Exam 3: Wednesday, April 29, 2015.

Final Exam: Monday, May 11, 2015, 8:05 - 10:05 PM.

Rooms for the Final Exam, and which section goes in which room, as follows:

Room	Sections
LH-1	1,4,5,6,7,9,15
LH-9	3,12
LH-10	8,11
LH-14	2,10,13,14

Note that the Add/Drop Deadline is Feb. 6, and the Withdrawal Deadline is April 3.

A detailed content of each exam will be determined one week before the exam, but we expect it to be as follows:

Exam 1: Sec. 6.1, 6.2*, 6.3*, 6.4*, 6.5, 6.6, 6.8.

Exam 2: Sec. 7.1 - 7.4, 7.8, 11.1.

Exam 3: 11.2 - 11.11, 8.1, 8.2.

The Final Exam will be comprehensive, covering the whole course, including material covered from chapter 10.

Important Note: No calculators or laptop computers will be allowed on exams.

Scientific calculators may be needed for some homework.

Schedule

Week 1: Jan. 26 - 30	6.1, 6.2, 6.3
Week 2: Feb. 2 - Feb. 6	6.4*, 6.5
Week 3: Feb. 9 - 13	6.6, 6.8
Week 4: Feb. 16 - 20	7.1, 7.2, Exam 1
Week 5: Feb. 23 - 27	7.3, 7.4
Week 6: Mar. 2 - Mar. 6	7.8, 11.1
Week 7: Mar. 9 - 13	11.2, 11.3
Week 8: Mar. 16 - 20	11.4, Review, Exam 2
Week 9: Mar. 23 - 27	11.5, 11.6
Week 10: Mar. 30 - Apr. 2	11.8
Week 11: Apr. 6 - 10	Spring Break
Week 12: Apr. 13 - 17	11.9, 11.10
Week 13: Apr. 20 - 24	11.11, 8.1, 8.2
Week 14: Apr. 27 - May 1	10.1, 10.2, Exam 3
Week 15: May 4 - 8	10.3, 10.4, Review
Week 16: May 11, 8:05-10:05 PM	Final Exam

Supplementary Materials and Links

Factorization of polynomials (Useful for working with Partial Fractions)

Useful Limits to Know

Guide to Checking Convergence/Divergence of Series

The following are pdf files with a polar coordinates grid (in radians or degrees) on which you can conveniently make graphs of functions given in polar coordinates.

Polar Coordinates Graph (radians)

Polar Coordinates Graph (degrees)

Visual Calculus - Step by step tutorial on the topics of our course.

For Calc II see:

An excellent source for math videos

Another excellent source for math videos

Integration: Techniques of Integration, Numerical Integration, Improper Integrals

Sequences, Series, Power Series

Cycloid

Calculus On the Web an online tutorial.

The math forum - various math resources. Check out the topics on calculus

MathWorld - more math resources.

Mathnerds - get hints on your math questions.

The archives - Copies of the Math 222 home page for previous semesters.

Math 404: Advanced Linear Algebra.

2015-12-28T18:20:44-04:00

Math 404: Advanced Linear Algebra.
Spring 2016

Instructor: Alex Feingold
Time:
Location:

Alex Feingold

2026-06-27T05:13:13-04:00

Alex Feingold

Professor
Ph.D., 1977, Yale University
At Binghamton since 1979
Areas of Interest: Algebra, Lie algebras and their representations, conformal field theory, piecewise isometry groups
Summary of research interests

Math Reviews list of published papers .
(Institutional subscription to MathSciNet is needed for viewing.)

E-mail:	feingold@binghamton.edu, alex@math.binghamton.edu
Office:	WH 324
Fax:	(607) 777-2450

Ph. D. Students:
- Joshua Carey, Spring, 2022
  Thesis: Branching rule decomposition of the level-1 $E_8^{(1)}$-module with respect to the irregular subalgebra $F_4^{(1)} \oplus G_2^{(1)}$
- Diego Penta, Spring, 2016
  Thesis: Decomposition of the Rank 3 Kac-Moody Lie Algebra F with Respect to the Rank 2 Hyperbolic Subalgebra Fib
- Christopher Mauriello, Spring, 2013
  Thesis: Branching Rule Decomposition of Irreducible Level-1 E₆⁽¹⁾-modules with respect to F₄⁽¹⁾
- Quincy Loney, Summer, 2012
  Thesis: Decomposition of Level-1 Representations of D₄⁽¹⁾ With Respect to its Subalgebra G₂⁽¹⁾ in the Spinor Construction
- Omar Saldarriaga, Summer, 2004
  Thesis: Fusion Algebras, Symmetric Polynomials, Orbits of Elementary N-Groups, and Rank-Level Duality
- Mike Weiner, Spring, 1994
  Thesis: Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Here's a link to my personal web page where you can find links to syllabi of my current and recent courses, links to pictures of my mathematical sculptures, links to the webpages I maintain for the Phi Beta Kappa liberal arts honor society, and for the Pi Mu Epsilon math honor society, as well as many other interesting links.