Dan Singer
Associate Professor
Department of Mathematics and Statistics
Minnesota State University, Mankato
Professional
Development Report for Fall 2012 – Spring 2013
Section
1: Teaching
I taught the following courses:
Fall 2012
Math 121-04 (Calculus I)
Math 121-05 (Calculus I)
Math 121-42 (Calculus I)
Spring 2013
Math 375 (Introduction to Discrete Mathematics)
Math 447/547 (Linear Algebra II)
Documentation:
Please follow the links to the course websites provided above for instructional materials: syllabuses, lecture notes, illustrations, Mathematica notebooks, homework assignments/hints/solutions, and exam study guides/solutions.
Highlights:
In Abstract Algebra I taught Galois Theory using Maureen Fenrick's textbook Introduction to the Galois Correspondence. Dr. Fenrick taught at Mankato until she retired a few years ago. I wrote extensive lecture notes based on her book and posted these online. I also worked out nearly every problem in the textbook in preparation for teaching this class. The lecture notes can be accessed online.
In Discrete Math I taught Polya's method for counting inequivalent graph colorings for the first time. I posted illustrations of graph colorings online, as well as lecture notes for several other topics presented in the course.
In Linear Algebra we worked through every problem of the textbook Linear Algebra Done Right by Sheldon Axler. I posted lecture notes for every chapter online, as well as several Mathematica notebooks devoted to Euclidean vector space computatons (Gram Schmidt, Orthogonal Projection, Least Squares Fit examples, etc).
In the Calculus sections I worked through old exams in practice sessions with students before every exam.
A
Low Point:
A few weeks into the graduate linear algebra class I discovered that a majority of students were copying solutions out of a solutions manual that is only supposed to be available to instructors by request. Of course, you can find everything on the Internet. So I had to caution my class about plagiarism and I was forced to change the grade scale to downgrade the homework contribution. To my chagrin, people continued to copy from the solutions manual (okay, “borrow” or “achieve inspiration”) throughout the remainder of the course. I got around this problem for the most part by giving substantial homework hints/sketches/complete solutions in class and having students fill in the details as a part of their homework. I am using this technique again this semester in Math 605 (Graph Theory) and will use it again next semester in Math 542 (Number theory).
Student Feedback:
I have summarized student comments in Spring 2013 and posted statistical summaries of student evaluations from Spring 2013 in the links below:
Strengths and Weaknesses Summarized Spring 2013
Statistical Summaries of Student Evaluations Spring 2013: Math 121-05 Math 375 Math 447/547
Section
2: Research
In Fall 2012 I gave a colloquium talk in the Department of Mathematics and Statistics describing the research I performed in Spring 2012, thanks to a one-class release from teaching at that time granted by the department. The title of the talk was A Problem in Combinatorial Linear Algebra and the abstract, narrative, and slide presentation can be accessed via the link provided in this sentence. I gave a variation of this talk at the Spring Meeting of the North Central Section of the Mathematical Association of America on Saturday, April 27, 2013.
In Summer 2013 I continued testing combinatorial conjectures related to my research using Mathematica. I have a wonderful conjecture regarding group actions on the set of binary trees that seems to extend Polya’s method of counting graphs with symmetries, but this will have to wait for Spring 2014 and a (hoped-for) one-class release from teaching.
Section
3: Continuing Preparation and Study
As indicated in Section 1, I wrote extensive lecture notes for Math 375 (Introduction to Discrete Mathematics), Math 447/547 (Linear Algebra II) , and Math 641 (Abstract Algebra). In the latter two courses I worked through almost every problem in the textbook before teaching the course so that I could supply useful homework hints and think about how to present the material to students. During Summer 2013 I read Goedel’s Proof by Nagel and Newman (New York University Press, 1958), an explication of Goedel’s paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." I also begain preparing notes on recursive functions and computable sets, central to the proof of Goedel’s incompletenes theorems. These are based on a series of lectures by B. Kim which I accessed online. My notes are a work in progress.
Section
4: Contributions to Student Growth and
Development
In addition to the handout Five Tips for Effective Studying in Mathematics Courses, which I have been handing out for a few years now in every course I teach, I wrote an additional handout called Surviving Calculus for my calculus sections. As indicated in Sections 1 and 3, I posted lecture notes, homework and exam solutions, illustrations, and Mathematica notebooks online for my students’ convenience. I conducted review sections for my calculus sections. In the graduate Linear Algebra course, which is preparation for the Masters Comprehensive Exam as well as foundational material for many topics in mathematics, I incorporated applications to differential equations, recurrence relations, finite fields, orthogonal projection and best fit, and combinatorial representation of determinants into the take-home exams. As I do every year, I helped students in office hours. I wrote letters of recommendation for Leah Lumley and Juna Shrestha.
Section
5: Service
I served on the Department Curriculum Committee and served both semesters as its representative to the CSET Curriculum Committee. I supplied Linear Algebra and Abstract Algebra problems for the Masters Comprehensive Exams in Mathematics and Mathematics Education, respectively. I served on Dr. Han Wu’s promotion committee and wrote a strong letter of support for him when his application hit a rough patch after being strongly endorsed by the committee and the department. I wrote the revised department course outlines for Math 121, Math 345 and Math 375.