```html Vitaly I. Voloshin — Teaching

Vitaly I. Voloshin — Teaching

Selected information about my teaching, courses, and teaching philosophy.


Courses taught

  1. Finite Mathematics ONLINE (Blackboard; Course Compass / MyMathLab by Pearson Education) (USA)
  2. Applied Discrete Mathematics (USA)
  3. Business Calculus (USA)
  4. Programming for mathematicians (C++) (USA)
  5. Discrete Mathematics (USA)
  6. Introduction to Graph Theory (USA)
  7. Algebraic Structures (USA)
  8. Probability and Statistics I, II (USA)
  9. Calculus II, III (USA)
  10. Introduction to Advanced Mathematics and Proof Technique (USA)
  11. Selected topics (Introduction to Coloring Theory) (USA)
  12. Selected topics (Introduction to Graph and Hypergraph Theory) (USA)
  13. Foundations of Mathematics (USA)
  14. Real Analysis (USA)
  15. Introduction to Graph and Hypergraph Theory (Italy, in Italian)
  16. Graph and Hypergraph Theory (Moldova, in Russian)
  17. Introductory Computer Science (Moldova, in Russian and Romanian)
  18. Data Base Management Systems (Moldova, in Russian and Romanian)
  19. Computer Aided Design (Moldova, in Russian)
  20. Programming Lab on Graph and Hypergraph Algorithms (Moldova, in Russian)
  21. Mathematical Programming (Moldova, in Russian)
  22. Information Theory (Moldova, in Russian)

Every year I supervised 3–5 annual theses and 2–5 master’s theses. I consulted three Ph.D. theses in Italy (one defended in 1996 received a special award of the Italian National Science Foundation in 1997; others defended in 2002 and 2003), consulted one master’s thesis in Italy (1998), and supervised three Ph.D. theses in Moldova (defended in 1998 and in 2000 (two theses)). All of these were in Mixed Hypergraph Coloring.

The efficiency of my teaching is certified by the USSR Diploma of Associate Professor, conferred by the State Committee on National Education of the USSR, Moscow, 1991.


Teaching philosophy

My teaching philosophy can be expressed by the following formula: interest + consecutive complication + competitiveness + individual approach.

In any course, the material should be presented in a consecutive-complication way for best understanding. First, the audience should understand the idea. There should be a reasonable balance between ideas and technical results. One idea costs more than 10 shallow theorems. Beauty of mathematics is in ideas; the beauty itself is an idea.

Competitiveness means that students must compete for better implementation of tasks. For example, in Programming for mathematicians (C++), one assignment was to program a game on graphs. To win the game, students competed using their own knowledge of theory, algorithms, and strategy, under the same initial conditions (graph, positions of players, and data structures). The winner received extra credit.

Another favorite assignment (in Discrete Mathematics) was to program an algorithm for planarity testing — only the strongest and most talented students were able to complete it on time.

In education, interest is the base of all and everything. I view surprise as a major component of interest. Very often, interest is rooted in contradictions between ordinary reasoning and new facts. A class was lost if it was not interesting for students. I consider this a personal defeat of a professor. Each course must not be very difficult, must not be very easy, but must be interesting.

In this respect (apart from careful exposition), historical and philosophical remarks, comments related to other sciences, real-life connections, and humor in the right places are relevant. They should be thought out in advance and collected throughout life.

Principles

Computer Science is a secondary area of my professional interests. Therefore, in teaching I pay special attention to connections with Computer Science and to computer education of students in Discrete Mathematics and Graph Theory. Over the last decades, Computer Science and its applications provided a major contribution to the development of these subjects, and in turn Computer Science is a major consumer of solutions coming from Discrete Mathematics and Graph Theory.

My belief is that teaching Discrete Mathematics and/or Graph Theory without using computers, algorithms, and applications is out of date and significantly less interesting and useful for students. In this context, graph algorithms and computer graphics — visualization of discrete structures and algorithms — represent the best playground. It is one thing to learn a graph algorithm from the textbook; it is a very different thing to implement the algorithm as a software project.

A particularly successful example is the Hypergraph Drawing and Optimization System, implemented by my students. It is a large program with multiple subprograms created by different students using a universal ideology and data structure developed for hypergraphs. It was designed for automatic drawings of hypergraphs and contains an open library of algorithms for computational optimization problems. Having and modifying the picture of a hypergraph on the screen, one can directly apply any algorithm from the library. The system was demonstrated at many international conferences and can be shown on my laptop.


Teaching in Illinois and Delaware

University of Illinois at Urbana–Champaign

As Visiting Professor (January–May 2002) in the Department of Mathematics, University of Illinois at Urbana–Champaign, I taught two courses: Introduction to Graph Theory (Math 312, section G1; parallel to the same course taught by D. West in the same term), and Calculus (Math 130, section E2). Both courses were taught for the first time.

Selected student comments (UIUC)

“…good at emphasizing the main point in ideas…”
“…clearly explains topics…”
“…very friendly and knows the material well…”
“…simply a general high quality of teaching…”
“…he explains things very clearly and logically…”
“…explains material with extreme care for students understanding and shows real passion for his work…”
“…Professor … was perhaps the best teacher I have had for ANY teaching at class…”

All evaluations (without exception) are available.

University of Delaware

In 2002–2003, at the Department of Mathematical Sciences of the University of Delaware, I taught two courses: Math 210 (Discrete Mathematics) and Math 243 (Calculus III). Anonymous final instructor and course evaluations were conducted in December 2002. All evaluations (without exception) are available.

Typical student comments (UD)

“…Dr. Voloshin ranks among the best math professors I’ve ever had…”
“…BEST MATH TEACHER I’VE HAD AT UD PERIOD.”
“This guy rocks! Best MATH210 teacher at the University. … runs the show.”
“Very nice professor, was a pleasure to be in class.”

Overall rating (“instructor as a teacher”) on Math210: excellent 58.8%, good 35.3%.
The same rating on Math243: excellent 54.5%, good 36.4%.


Teaching in Alabama (Troy University)

Fall 2003

Spring 2004

Summer 2004

Fall 2004

Typical Troy University student comments

“Clear lectures, friendly attitude, always ready to help, learn a lot — excellent teacher!”
“Outstanding teacher!”
“Dr. Voloshin is a great instructor. He really cares about how you do in his class…”
“The course was very well planned! … Dr. Voloshin’s way of teaching is very strategic and organized.”
“Dr. Voloshin pushed for the best out of every student.”
“The grading system was very fair.”

Spring 2005

Typical student comments (Spring 2005)

“Help me a lot! Great Professor.”
“He teaches very well.”
“I love his way of teaching.”
“Dr. Voloshin is a great teacher, who is willing to help his students.”
“Great job, hope to see you in the Fall.”

Summer 2005

Fall 2005 (upper level)

Spring 2006


Teaching ONLINE (from End-of-Course evaluations)

“This instructor was wonderful. I really felt that he cared about my personal well-being during the course…”
“Dr. Voloshin really stayed involved with the students throughout the entire course to ensure we were successful!”
“He was always on top of everything and always emailed me back usually within a couple hours.”
“The reminders of assignments were helpful and the instructor was always willing to answer questions!”
“The teacher’s interaction with the students is the most I have had in any of my on-line classes.”
“This instructor is excellent! He keeps us VERY well informed and responds to our e-mails in a very timely manner.”
“Dr. Voloshin was probably the most involved and most interested instructor I've had in years.”
“Dr. Voloshin is the BEST!”
“VOLOSHIN IS AN AWESOME TEACHER!!!!!”
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