Myron Minn-Thu-AyeTeaching Portfolio

Contents

Summary of Courses Taught 2

Course Evaluation Data 3

Course Evaluation Comments 9

Teaching Awards 15

Sample Lesson 16

Sample Syllabus 21

1

Summary of Courses Taught

University of Connecticut

• MATH 1070Q: Mathematics for Business and Economics (large lecture and hybrid online)

• MATH 1132Q: Calculus II (large lecture)

• MATH 1151Q: Honors Calculus I (flipped classroom)

• MATH 1152Q: Honors Calculus II (flipped classroom)

• MATH 2110Q: Multivariable Calculus

• MATH 2360Q: Geometry

• MATH 2710: Transition to Advanced Mathematics

• MATH 3160: Probability

• MATH 3230: Abstract Algebra I (inquiry-based learning)

• MATH 3240: Introduction to Number Theory (inquiry-based learning)

• MATH 5000: Mathematical Pedagogy

Louisiana State University

• MATH 1021: College Algebra

• MATH 1022: Plane Trigonometry

• MATH 1023: College Algebra & Trigonometry

• MATH 1100: The Nature of Mathematics (for non-science students)

• MATH 1201: Number Sense and Open-Ended Problem Solving (for education students)

• MATH 1550: Calculus I

• MATH 1552: Calculus II

2

Course Evaluation Data

This is a summary of all evaluations I have received at the University of Connecticut and LouisianaState University in reverse chronological order. The data is given in parts due to changes in theformat of evaluations within and between institutions. A complete copy of all individual evaluationswith comments is available upon request.

University of Connecticut

Evaluation on a scale of 1-5:1 - Strongly Disagree / Poor2 - Disagree / Fair3 - Neither Agree nor Disagree / Good4 - Agree / Very Good5 - Strongly Agree / Excellent

Questions:1. The instructor presented the course material clearly.2. The instructor was well prepared for class.3. The instructor responded to questions adequately.4. The instructor stimulated interest in the subject.5. The instructor showed interest in helping students learn.6. The instructor gave clear assignments.7. The instructor was accessible to students.8. The instructor gave useful feedback on my performance.9. The instructor returned graded work in a reasonable amount of time.10. The instructor used class time effectively.11. The instructor treated all students with respect.12. The instructor graded fairly.13. The instructor’s teaching methods promoted student learning.14. What is your overall rating of this instructor’s teaching?

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Summer 2015MATH 3160 4.8 5.0 5.0 4.7 5.0 4.6 4.8 4.7 4.8 5.0 5.0 5.0 5.0 5.0Probability

Spring 2015MATH 1070Q 4.3 4.3 4.1 4.0 4.3 4.3 4.2 3.9 4.3 4.3 4.3 4.3 4.2 3.9Math for Business

Spring 2015MATH 1152Q 4.9 4.9 4.9 4.9 4.9 5.0 4.9 4.8 4.9 4.8 4.9 4.9 4.9 4.9Honors Calculus II

Spring 2015MATH 3240 4.8 4.8 4.8 4.3 4.8 4.8 4.8 4.7 4.8 4.5 4.8 4.5 4.5 4.3Number Theory

3

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Fall 2014MATH 1070Q 4.5 4.6 4.4 4.3 4.5 4.5 4.3 3.9 4.4 4.4 4.5 4.5 4.5 4.1Math for Business

Fall 2014MATH 1151Q 4.4 4.9 4.7 4.6 4.8 4.8 4.8 4.5 4.9 4.3 4.9 4.7 4.5 4.6Honors Calculus I

Fall 2014MATH 2360Q 4.6 4.6 4.5 4.7 4.5 4.5 4.5 4.3 4.5 4.5 4.6 4.4 4.5 4.7Geometry

Spring 2014MATH 1070Q 4.5 4.5 4.3 4.1 4.4 4.6 4.2 4.0 4.1 4.4 4.5 4.6 4.3 4.0Math for Business

Spring 2014MATH 2110Q 4.9 4.9 4.8 4.6 4.9 4.8 4.7 4.6 4.9 4.8 4.9 4.8 4.7 4.8Multivariable Calculus

Spring 2014MATH 2710Q 4.8 4.9 4.9 4.3 4.6 4.7 4.8 4.8 4.9 4.7 4.8 4.6 4.5 4.7Transition to Adv Math

Fall 2013MATH 1070Q 4.5 4.6 4.6 4.4 4.6 4.5 4.6 4.2 4.5 4.4 4.7 4.5 4.4 4.1Math for Business

Fall 2013MATH 2110Q 4.8 4.9 4.9 4.7 4.9 4.7 4.8 4.7 4.9 4.8 4.9 4.7 4.8 4.9Multivariable Calculus

4

Louisiana State University

Spring 2013

Evaluation on a scale of 1-4:1 - Strongly Disagree2 - Disagree3 - Agree4 - Strongly Agree

Questions:1. In the first week of class, the instructor provided documents and information that clearly

explained the course content, assignments, grading and other important policies.2. The course materials, exams, projects and/or papers in this class required me to think critically.3. The instructor welcomed questions and other class participation.4. The instructor was enthusiastic with respect to the subject matter.5. The instructor was available for consultation and helpful during office hours.6. The instructor arrived on time for class and used the full class period allotted.7. In order to get good grades on the tests and assignments, I had to know the course materials

outlined in the syllabus and discussed in class.8. The instructor’s presentations were informative.9. Overall, the instructor is an effective teacher.10. Overall, I have learned or benefitted from this course.11. Average [Average for all 1000-level mathematics courses that semester in brackets].

Question 1 2 3 4 5 6 7 8 9 10 11

Spring 2013MATH 1552 3.97 3.86 3.97 4.00 3.97 4.00 3.90 4.00 4.00 3.96 3.96 [3.55]Calculus II

5

Fall 2011 to Fall 2012

Evaluation on a scale of 1-5:1 - Strongly Disagree2 - Disagree3 - Undecided4 - Agree5 - Strongly Agree

Questions:1. The teacher motivated me to do my best2. The teacher communicated clearly and understandably.3. The teacher was concerned about student learning.4. The teacher was well-prepared for each class.5. The teacher demonstrated respect for the students.6. The teacher’s coverage of the material in the classroom provided me with a good base of

knowledge and enough in-class examples to prepare me for the assignments in MyMathLab.7. The teacher budgeted class time well between announcements, conceptual explanations, and

skill examples.8. The teacher had excellent blackboard / document camera technique.9. The teacher posted grades in Moodle within a reasonable amount of time.10. Overall, the teacher was effective.11. Average.

Question 1 2 3 4 5 6 7 8 9 10 11

Fall 2012MATH 1023 4.24 4.48 4.52 4.52 4.71 4.33 4.43 4.33 4.19 4.48 4.42Pre-Calculus

Spring 2012MATH 1021 4.36 4.57 4.52 4.50 4.63 3.77 4.02 3.86 4.32 4.48 4.30College Algebra

Fall 2011MATH 1021 4.40 4.49 4.58 4.66 4.66 4.27 4.31 4.26 4.53 4.62 4.48College Algebra

6

Spring 2010 to Spring 2011

Evaluation on a scale of 1-4:1 - Strongly Disagree2 - Disagree3 - Agree4 - Strongly Agree

Questions:1. In the first week of class, the instructor provided documents and information that clearly

explained the course content, assignments, grading and other important policies.2. The course materials, exams, projects and/or papers in this class required me to think critically.3. The instructor welcomed questions and other class participation.4. The instructor was enthusiastic with respect to the subject matter.5. The instructor was available for consultation and helpful during office hours.6. The instructor arrived on time for class and used the full class period allotted.7. In order to get good grades on the tests and assignments, I had to know the course materials

outlined in the syllabus and discussed in class.8. The instructor’s presentations were informative.9. Overall, the instructor is an effective teacher.10. Overall, I have learned or benefitted from this course.11. Average [Average for all 1000-level mathematics courses that semester in brackets].

Question 1 2 3 4 5 6 7 8 9 10 11

Spring 2010MATH 1201 3.84 3.64 3.73 3.88 3.79 3.96 3.76 3.72 3.76 3.62 3.79 [3.55]Math. for Elem.Ed. Majors

Fall 2010MATH 1550 4.00 3.77 4.00 4.00 3.91 4.00 3.95 3.91 3.91 3.86 3.94 [3.55]Calculus I

Spring 2011MATH 1552 3.93 3.86 3.93 4.00 3.96 3.93 3.89 4.00 3.96 4.00 3.94 [3.56]Calculus II

7

Fall 2008 to Fall 2009

Evaluation on a scale of 1-5:1 - Strongly Disagree2 - Disagree3 - Undecided4 - Agree5 - Strongly Agree

Questions:1. The instructor motivated me to do my best.2. I have learned a lot in this class.3. The instructor clearly communicated the learning objectives of the course.4. The instructor communicated clearly and understandably.5. The instructor was available for assistance outside the course.6. The instructor was concerned about student learning.7. The instructor was well-prepared for each class.8. The graded work reflected important aspects of the course.9. The instructor demonstrated respect for the students.10. Overall, the instructor was an effective teacher.11. Average [Average for all sections of the same course that semester in brackets].

Question 1 2 3 4 5 6 7 8 9 10 11

Fall 2008MATH 1022 4.38 4.14 4.48 4.48 4.71 4.52 4.52 4.10 4.71 4.62 4.4 [3.8]Trigonometry

Spring 2009MATH 1550 4.87 4.87 4.87 4.91 4.92 4.91 4.88 4.78 4.96 4.88 4.9 [4.4]Calculus I

Fall 2009MATH 1552 4.52 4.66 4.66 4.76 4.79 4.62 4.86 4.66 4.79 4.72 4.8 [4.4]Calculus II

8

Course Evaluation Comments

This is a selection of student comments from courses at the University of Connecticut and LouisianaState University, listed in reverse chronological order. I have included comments that I am proud of,that touch upon aspects of teaching that are important to me, or that provide enlightening critiques.All comments have been transcribed as written. A complete copy of all individual evaluations withcomments is available upon request.

University of Connecticut

MATH 3160, Probability, Summer 2015

• “Myron is a very good teacher. His good attitude and cheerfulness make the 2 hour classmuch more bearable. After being at UConn for 6 semesters he is definetly in the top 10 ofprofessors I have had. The class is well organized, and he gives many example problems thatare well thought out which really highlight the important concepts of the course. I also likethe practice worksheets that we do in class, I find those to be helpful and a good way to learn.Overall a well taught course!”

• “he lectured and explained concepts very well, but the amount of in class practice and howmuch Myron explained the problems that we did was extremely helpful. especially during asummer class that crams so much material so fast, having in class practice was very helpful”

• “Group assignments were the best! Definitely helps to discuss this sort of material.”

MATH 1070Q, Mathematics for Business and Economics, Spring 2015

• “I really liked how professor Myron always was emailing us and welcomed us to office hours.some professors don’t really like students coming to them if they have a ta and professorMyron was the opposite. you can tell he really cares for the students to learn and enjoyswhat he teaches”

• “Taking the course online made it possible to always have the lecture at my fingertips. Ithink this is why I was able to do so well on exams. Also the online lectures were in depthand made me feel a connection between student and professor.”

• “I wish the lectures included harder examples. Most of the lecture examples were very easycompared to the WebAssign problems.”

MATH 1152Q, Honors Calculus II, Spring 2015

• “I really liked learning in small groups and working together during class time. The videolectures were also really good, it helped save time during class that we could spend practicingproblems on our own.”

• “Myron taught this course in such a way that promoted learning in a completely non-intimidating way, that also fostered peer interactions with group work all while achievingthe goal of having students successfully learn the material.”

• “Myron is passionate about the subject. He wants his students to succeed and it shows. Heworks with students to ensure that they understand the concepts and helps guide them therewithout flat out giving them the answers.”

9

MATH 3240, Introduction to Number Theory, Spring 2015

• “The structure and clearness of the material was definitely the most positive aspect of Myron’steaching. The outline was very clear and followed a logical order. Each section of the coursebuilt on the previous section, and the connections between the units were made very clear.Myron also always made himself available to answer questions in class and outside of class.He doesn’t just give answers to questions, but he asks questions to stimulate student thinking.Overall, Myron is a great person and resource to have in the UConn Math Dept.”

• “Myron made an effort to not have this course be lecture-based and rather be focused on ourwork. This made the class more interesting since we had a chance to work in groups anddiscuss proofs.”

MATH 1070Q, Mathematics for Business and Economics, Fall 2014

• “Professor Myron Minn-Thu-Aye always made himself available to his students and encour-aged us to reach out if we ever had any questions.”

• “He explained everything step by step, even if it was something simple. I really, reallyappreciated that. And he always mentioned how he was available if we had any questions.”

• “This was an online class and all of the videos on the lessons were extremely thorough andwell organized. I feel that the videos presented much more information than what would beable to be covered in an in-class session and did so in a very effective and helpful way.”

MATH 1151Q, Honors Calculus I, Fall 2014

• “Myron was always extremely approachable and was willing to help students on any issuesthey had. This helped create a great environment to learn in and took a lot of the stress ofsuch a difficult course off the student’s shoulders. I learned more in this calc class than anymath class I had taken in the past.”

• “Myron was clearly very knowledgeable on the subject and presented the information in avery clear way that ensured every student was following along before moving on with thelesson. It was also very helpful to see why certain properties and principles worked insteadof just accepting them as fact.”

• “The online lecture videos were incredibly helpful as a resource to look back on throughoutthe semester or just as a reference in general. Everything was presented in a way assumingno previous knowledge of the subject, which helped level the playing field for students.”

• “To improve effectiveness, the instructor can work through more difficult examples with theclass, rather than mostly going over simple examples and leaving more complex problems forworksheets.”

10

MATH 2360Q, Geometry, Fall 2014

• “Myron’s personality was great, it was also nice walking into a classroom with such a goodatmosphere. His notes were very organized, and he presented the material clearly, and whenI did have questions he answered them well. Also, it was really helpful that he was alwaysavailable via email when I was working on the homework assignments, and that he wouldgive helpful hints on tough homework problems. Also, it was SO helpful that our exams weretake-home- please keep doing this!”

• “Very good speaking voice, well organized notes on the board. Doing proofs step by step isvery helpful. Short breaks in the middle of class allow students to recharge and should beimplemented in all 1 hr+ sessions. Geometry was the class I’ve been dreading to take butthe instructor made the class great”

• “Myron taught this class clearly and with great ease. He is extremely knowledgeable aboutthe subject and enjoyed sharing that knowledge with each of us. He was open to all questionsat any point in the lecture, his handwriting was clear, neat and easy to follow, and he wasalways available outside of class when I needed help. Assignments were also returned in aprompt and often speedy fashion. This made studying and reviewing material on a weeklybasis much more manageable. Myron was one of my favorite math instructors thus far and Ihope to be taking more classes with him in the future.”

MATH 1070Q, Mathematics for Business and Economics, Spring 2014

• “Everything was well organized and laid out well. Even if we got behind it was easy to seewhat needed to be done in the class. Videos were straight to the point, no annoying off topicconversations. The Videos were not too long, which was good because it kept everythingsimple and clear/to the point.”

• “It was online, but he was always available for office hours or if you ever wanted to meet withhim and was very helpful.”

• “Although it was online, the professor seemed as if he cared much for his students.”

MATH 2110Q, Multivariable Calculus, Spring 2014

• “He really made sure to show us how he cared about us as people. He learned all our nameson the first day, even though there were almost forty of us! I think it made a big differencethat he knew who each of us were.”

• “Very willing to help you learn and take the time to go over anything you didn’t understand.”

• “He came to class every day excited to teach, and that made an incredible impact on themood of the class. I always felt enthused by the instructor and I was always ready to learn.”

• “He reviewed what we learned in the last class at the beginning of each new class, whichhelped me organize what I learned in my mind.”

11

MATH 2710, Transition to Advanced Mathematics, Spring 2014

• “Myron presented the material in an easy-to-understand way and checked if students hadquestions often. He made sure everyone understood every aspect of the material beforemoving on to cover something new.”

• “The lectures were presented in a way that made the material easy to understand and pro-moted the problem-solving aspect that was needed to figure out the proofs in the homeworkassignments.”

MATH 1070Q, Mathematics for Business and Economics, Fall 2013

• “He was really enthusiastic about the material and was really clear when teaching. He madesure that everyone understood the material and was always willing to answer questions. Hewas really great at explaining everything and made sure that you understood what he wassaying. Really great energy while teaching.”

• “Myron connected well with his students and made sure all questions were answered beforemoving on and explained each example very well with greatly detailed notes which helped mein the future.”

• “One thing that this professor can do is try to define more of the terms that were taught ineach lecture. The examples were helpful, but there should be more summarizing as well.”

MATH 2110Q, Multivariable Calculus, Fall 2013

• “Myron was always clear and checked with everyone if we understood what he wrote down.He gave multiple examples and was friendly and respectful to everybody. Made learningeasier and efficient.”

• “Myron was always prepared, extremely enthusiastic, and was always willing to meet withstudents and take time out of his schedule to make sure we were understanding the material.Occasionally, Myron would send out emails encouraging the class to remained focused anduse certain study tips to help us retain the material.”

• “He was relate-able and dedicated to his wok. He was willing to work with me on unrelatedsubjects just to stimulate interest.”

• “We would learn a lot in only a matter of an hour and fifteen minutes so maybe a quickoverview of what we learned at the end of class would solidify what concepts apply to whichproblems.”

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Louisiana State University

MATH 1552, Calculus II, Spring 2013

• “Mr. Myron was incredibly enthusiastic and helpful and his lessons were well-explained andeasily digestible. I had a very positive experience in Calculus 1552 and wouldn’t change athing about the class.”

• “He was very approachable and friendly, taught at a good pace. I always understood hishandwriting and he spoke clearly. Something I would watch would be the rambling, it mademe lose focus. Other than that great class!”

MATH 1023, College Algebra & Trigonometry, Fall 2012

• “He was an excellent teacher throughout the semester. Very clear on explaining hard con-cepts!”

• “Very happy. Very helpful. Awesome instructor.”

MATH 1021, College Algebra, Spring 2012

• “I really enjoyed this class more than first semester Math 1021. The teacher was a great helpand was always checking on his students during class to see if they needed help and to justtalk to them about what was on thier mind for this class. He was an awesome teacher andvery effective!”

• “Great teacher; genuinely cared for his students & learning; very nice & understanding;always willing to help. I don’t like math, but my teacher made it as good as it could be. Veryapproachable and respectable.”

MATH 1021, College Algebra, Fall 2011

• “The instructor was very clear and concice. He did an excellent job presenting the material”

• “I have never been a strong math student, so coming into college math I was very nervous. Iheard the teachers didn’t care and weren’t helpful but Myron was very dedicated and reallymade me feel like he cared. I’m very thankful for that and never have done this well in anyclass.”

• “Excellent job explaining the concepts in a reasonable manner and actually writing downwhat we should do in words rather than just putting up examples on the board”

MATH 1552, Calculus II, Spring 2011

• “Always made himself available. Detailed e-mail responses were extremely helpful”

• “This class was great. I was good to have a young and excited teacher. The quizzes eachday really helped with the overall learning of the material and prepared me well for the test.Thanks a lot man!!”

• “great teacher, very knowledgeable of info, fair tests, cared about us students”

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MATH 1550, Calculus I, Fall 2010

• “Having had taken this class twice already, I assumed that I would just get through it thistime without learning much more. I was wrong. The way the teacher presented informationmade it ‘click’ in my head, making it able for me to succeed in this class much more than Iwould have thought. I thank you greatly for a wonderful semester.”

• “I thought Myron was a very effective and enthusiastic calculus teacher. I really liked theinteractiveness of the class and he is always willing to help. Answered all my questionspromptly and accurately.”

• “The class was surprisingly fun and helpful w/some everyday situations. Myron is one ofthe best teachers I’ve ever had and makes this class capable for anyone to take. He honestlylistens to his students and tries hard to ensure all understand and are participating. I haveno idea what could be changed to make it better.”

MATH 1201, Number Sense and Open-Ended Problem Solving, Spring 2010

• “Myron was a great teacher! Always enthusiastic and wanted us to do well in the class.”

• “Having daily homework helped me stay on task in the course. Instructor was very under-standable, helpful, and an overall GREAT teacher. I really enjoyed this class and I hatemath.”

• “He was very enthusiastic about the subject. I like that he was available for extra helpoutside of class, but I think we should have went over homework more in class. Overall, greatteaching”

MATH 1552, Calculus II, Fall 2009

• “Great teacher! I wish I had had him for Calc 1! Sometimes went/spoke too quickly, but Ialways got the material. Availability outside of class was excellent! Myron really cared aboutthe students & their success in his and all other classes. He worked around times/difficultweeks for people. Awesome guy!!”

• “I enjoyed your class a lot! But sometimes your lectures were a little too high-energy for me,but that’s more of a personal preference. Good luck in life!”

• “This was such a good class. You hear horror stories about sequences and series before youtake Calc 2 but it wasn’t scary. He was great at teaching the material and making sure weunderstood it. Don’t become lazy when you get older Myron cause seriously you are the bestteacher I’ve ever had. This is a hard class but the homework while a lot was so helpful. Youreally helped me. Thank you!”

MATH 1550, Calculus I, Spring 2009

• “It was a great learning experience, Myron sparked an interest in math for me, and was anexcellent teacher.”

• “I really enjoyed this class, because I could ask questions and he was a great listener.”

• “Myron was absolutely the best teacher I have ever (and I mean ever) had. He was extremelyenthusiastic and really knew how to communicate on our level. He was also really good aboutmaking sure that everyone in the class was understanding the material!!”

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Teaching Awards

Certificate of Teaching Excellence (Fall 2012, Fall 2011, Fall 2009, Fall 2008)

Presented each semester by the LSU Department of Mathematics to recognize a small group of grad-uate students for teaching excellence. A graduate student can be awarded at most one Certificateof Teaching Excellence each academic year.

LSU Alumni Association Teaching Assistant Award (2011)

Presented annually by LSU to one graduate student or outstanding contribution to the university’steaching mission.

David Oxley Graduate Student Teaching Award (Fall 2010, Spring 2009)

Presented by the LSU Department of Mathematics for outstanding teaching by one junior graduatestudent each spring and one senior graduate student each fall. A graduate student can win thejunior award and senior award at most once each.

Certificate for Dedication to Instruction (Fall 2008)

Presented by the LSU Alpha Lambda Delta Freshman Honor Society to instructors who have madea positive contribution to students’ first-year studies.

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Sample Lesson

The following is an example of a complete lesson consisting of:

1. The slides from a video lecture introducing the topic. The students are provided with ahandout that includes blank spaces that they can fill in as they follow along with the video.The video can be found at http://www.movenote.com/v/m2GLg2ydAiqh8.

2. The pre-class quiz that is used to hold students accountable for watching the video lectureand preparing for further work in class, and to allow them to ask any questions that aroseduring the video.

3. The worksheet that students work on in groups during class to reinforce concepts from thevideo and extend their knowledge and understanding of the topic.

Lecture Slides

Alternative coordinate systems

Polar coordinates give us another way ofdescribing points in the plane.

Rather than giving x- and y -coordinates ashorizontal and vertical distances from theorigin, polar coordinates specify a radius r ,which gives the distance from the origin, andan angle ✓, which gives direction.

Examples:

When plotting points in polar coordinates, wethink of a circular web instead of a grid(imagine the grid wrapped around the origin):

For example, compare y = 1 and r = 1.

Similarly, compare y = cos (6x) + 2 andr = cos (6✓) + 2

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Converting between polar and Cartesian coordinates

cos ✓ = xr

so x = r cos ✓Similarly, y = r sin ✓

1� Find the Cartesian coordinates of the point(7, 3⇡

4) given in polar coordinates.

x = r cos ✓ = 7 cos 3⇡4

= 7⇣�

p2

2

⌘= � 7

p2

2

y = r sin ✓ = 7 sin 3⇡4

= 7⇣p

22

⌘= 7

p2

2

By the Pythagorean Theorem,r2 = x2 + y2 so r =

px2 + y2

Also, tan ✓ = yx

so ↵ = tan�1�� yx

��, where ↵ isthe acute angle between the ray representing✓ and the x-axis. The value of ✓ depends onwhich quadrant it is in.

2� Find the polar coordinates of the point(�3

p3,�3) given in Cartesian coordinates.

r =p

x2 + y2 =p

27 + 9 = 6

↵ = tan�1��� �3�3

p3

��� = tan�1⇣

1p3

⌘= ⇡

6

By looking at the Cartesian coordinates, weknow ✓ is in quadrant III since both x and yare negative. So ✓ = ⇡ + ↵ = ⇡ + ⇡

6= 7⇡

6.

Polar curves

3� Sketch the curve r = 2 sin ✓

Let’s plot points:✓ r0 0⇡6

1⇡4

p2 ⇡ 1.4

⇡3

p3 ⇡ 1.7

⇡2

2

When ⇡ < ✓ < 2⇡, r = sin ✓ is negative, sothe corresponding points are above the x-axis,and the curve is traced again.

4� Sketch the curve r = 1 + 2 cos ✓

✓ r0 1 + 2 = 3⇡6

1 +p

3 ⇡ 2.7⇡4

1 +p

2 ⇡ 2.4⇡3

1 + 1 = 2⇡2

1 + 0 = 1

✓ r2⇡3

1 � 1 = 03⇡4

1 �p

2 ⇡ �0.45⇡6

1 �p

3 ⇡ �0.7

⇡ 1 � 2 = �1

5� The curve r = 1 + 2 sin ✓ should look similarto the curve in Example 4�. How will it bedi↵erent?

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Pre-Class Quiz

MATH 1152Q - Honors Calculus II - Section 2Spring 2015

10.3 Pre-Class Quiz

Complete before class on Monday, March 23rd

Submit your answers online at http://goo.gl/forms/QcslrryuoC.

1) For the point (12, 5π3 ) given in polar coordinates, find its Cartesian coordinates (x, y). (Enterdecimal answers rounded to two decimal places).

2) For the point (−7, 7) given in Cartesian coordinates, find its polar coordinates (r, θ). (Enterdecimal answers rounded to two decimal places).

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Worksheet

MATH 1152Q - Honors Calculus II - Section 2Spring 2015

10.3 WORKSHEET

Converting from polar (r, θ) to Cartesian (x, y) coordinatesx = r cos θy = r sin θ

Converting from Cartesian (x, y) to polar (r, θ) coordinatesr =

√x2 + y2

α = tan−1| yx |, where α is the acute angle between the x-axis and the ray corresponding to θ.

10.3.a) The following points are given in polar coordinates. Plot each point, and find its Cartesiancoordinates.

(i) (5, 4π3 )

(ii) (2, 17π6 )

(iii) (−1,−5π4 )

10.3.b) Consider the point with Cartesian coordinates (−12, 4√

3).

(i) Find polar coordinates for this point, and plot it.

(ii) Find polar coordinates for this point where π < θ < 2π.

(iii) Find polar coordinates for this point where θ > 2π.

(iv) Find polar coordinates for this point where r < 0 and θ < 0.

10.3.c) Sketch the graph of r = θ. How would the graphs of r = 12θ and r = 2θ differ from the one

you have sketched?

10.3.d) Recall the graphs of r = 2 sin θ and r = 1 + 2 cos θ from the 10.3 video. Without plottingany points, sketch the graphs of r = 2 cos θ and r = 1 + 2 sin θ (they should lthe same shape as thecurves above but are positioned and oriented differently—the graphs are shifted and/or rotated).

10.3.e) A curve of the form r = a+ b sin θ or r = a+ b cos θ (note that a and b could be negative)is called a limacon. For example, r = 1 + 2 cos θ and r = 1 + 2 sin θ are limacons with inner loops.

(i) Plot points and sketch r = 3 + sin θ. This is an example of a limacon without an inner loop.

(ii) What must be true about a and b for a limacon to have an inner loop?

(iii) Sketch r = 2− 2 sin θ

(iv) Sketch r = −3 + 4 cos θ

(v) Sketch r = 1− 5 cos θ

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10.3.f) Find polar equations of the form r = f(θ) for the following lines.

(i) y = 4

(ii) x = −1

(iii) y = 5x

(iv) y = −x− 3

10.3.g) Sketch the graph of r = sin (2θ) by plotting points for θ = 0, π6 ,π4 ,

π3 ,

π2 ,

2π3 ,

3π4 ,

5π6 , π (this

will not give the complete curve, but you should be able to guess what the rest of it looks like).

10.3.h) Sketch the graph of r = cos (3θ) by plotting points for θ = 0, π6 ,π4 ,

π3 ,

π2 ,

2π3 ,

3π4 ,

5π6 , π (this

should give a complete image of the curve).

10.3.i) A curve of the form r = sin (nθ) or r = cos (nθ) where n > 1 is called a rose.

(i) How many petals does r = cos (3θ) have, and how many times is the curve traced when θgoes from 0 to 2π?

(ii) How many petals does r = sin (2θ) have, and how many times is the curve traced when θ goesfrom 0 to 2π?

(iii) Sketch r = cos (4θ)

(iv) Sketch r = sin (5θ)

10.3.j*) Sketch each of the following curves (you do not need to show any work)

(i) r = 3− 2 sin θ

(ii) θ = 5π3

(iii) r = sin (6θ)

(iv) r = −2− 4 cos θ

(v) r = 3 + 3 cos θ

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Sample Syllabus

MATH 3230: Abstract Algebra IFall 2015

Class Meetings: MWF 10:10-11:00 in MSB 307My Name: Myron Minn-Thu-AyeOffice: MSB 424Office Hours: Mondays 9:00-10:00 and 12:30-2:00,

Wednesdays 12:30-2:00 and 3:30-5:30E-mail: myron.minn-thu-aye@uconn.eduTextbook: Contemporary Abstract Algebra (7/e or 8/e), Gallian

Course description. Algebra is the study of structure in mathematics. We can use it to describesymmetry in all of its beautiful forms, study generalizations of familiar number systems, find pat-terns in infinite-dimensional geometric objects; the list goes on. Our goal is to learn why algebraicstructures might be interesting to us, and how to develop a deep understanding of these structures.

Inquiry-based learning. The central theme in all of our course activities is inquiry-based learn-ing (IBL). This is a student-centered and student-driven approach that will involve minimal to nolecturing by me, your professor. Engaging in IBL means you will be actively learning mathematicsby experimenting with new concepts, creating terminology, identifying patterns, asking questions,explaining your thoughts, conjecturing and proving theorems, and being confused and frustrated attimes (this is important!). I am your faithful guide on this journey, rarely providing quick or easyanswers, but always there for support and mentorship as you traverse the sometimes unpredictableterrain of mathematical exploration.

Pre-class and group work. During class, we will often discuss mathematics in small groups—this is designed to provide an environment where you can distill and express your own thoughts,generate new ideas, and find meaning in the mathematics we are learning. You will also be askedto share and present your work. Your participation grade will be based upon your various contri-butions to our class’ understanding, which will involve explaining both what you know and whatyou don’t. For these discussions to be productive, we need to have ideas to talk about to beginwith. Preparation before class is key, and may involve readings from our textbook or handouts,explorations of examples and conjectures, or work towards proofs of theorems. Always be preparedto discuss your work and your perspectives with your classmates!

Journaling. We will be keeping an online journal to record and reflect on our experiences thissemester. I will be writing an entry approximately once a week (at least every other week), andstudents will take turns contributing an entry after each class. Your entry should be personal andprovide insight into your own experience of the course, rather than a summary of our activities onthat day. You might touch upon the day’s highs and lows, successes and breakthroughs, failuresand frustrations; comment on any thoughts and emotions you had, or anything from class thatstood out to you or had an impact on you. Journal entries will count towards your participationgrade. The journal entry for each class meeting will always be due at midnight before our nextmeeting.

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Homework. There will be written homework assignments due every two weeks beginning on Fri-day, September 11th; homework is due at the beginning of class on these days. Some homeworkexercises will already have been discussed and perhaps presented in class. You are expected tosubmit, to the best of your ability, proofs that are cogent, clear, and well-organized. Rememberthat creating and constructing mathematical arguments takes time. This is a challenging course,and it will be even more so without collaboration with your colleagues. Discussing your work withme and your classmates will be really helpful.

Exams. We will have two take-home exams over the course of the semester. Our midterm examwill be from Friday, October 16th through Monday, October 19th, while our final exam will beginon Friday, December 11th, and will be due two days after our scheduled final exam time. Dur-ing exams you will be allowed to consult any materials from our course, including our textbook,handouts and worksheets, your own notes, and previous homework assignments. No materials fromoutside of our course are allowed.

Grading. Grades will be determined roughly as follows:Homework 25%Participation 25%Midterm Exam 25%Final Exam 25%

Academic Honesty. Collaboration on homework exercises is allowed and encouraged, but youmust write up your submissions based only on your own understanding. Journal entries must becompleted on your own without any discussion with me or your classmates. During exams, nocommunication between students is allowed. Any violation of this policy only undermines the goalsof our class and serves as a detriment to students’ learning.

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