Jovan Žigić
Email: Jovan.Zigic (at) duny.edu
Languages: Fluent in English and Serbian, Conversational in French and Spanish
I am an Assistant Professor of Mathematics and Physics at Dominican University in Orangeburg, New York, and a PhD candidate in Computational Science and Engineering at McMaster University. I have a Master's degree in Mathematics and Bachelor's degrees in Finance and Mathematics. My mathematical research has been focused in numerical analysis, optimization, computational fluid dynamics, and model reduction of dynamical systems.
This website is designed as a database for my scientific and professional activities.
"The most important thing in life is not the triumph, but the struggle; the essential thing is not to have conquered, but to have fought well."
“L'important dans la vie, ce n'est point le triomphe, mais le combat. L'essentiel n'est pas d'avoir vaincu, mais de s'être bien battu.”
- Baron Pierre de Coubertin
Learning Resources for Mathematics:
For foundational topics (up to undergraduate mathematics), Khan Academy and OpenStax
For advanced topics (up to graduate mathematics), Open Math Notes, RealNotComplex, Class Central and Open Culture
How to Successfully Learn Mathematics:
The main ingredients determining one's success in anything they do: Curiosity, Confidence, Patience and Effort.
a. Mathematical proficiency has five strands (source):
Understanding: Comprehending mathematical concepts, operations, and relations—knowing what mathematical symbols, diagrams, and procedures mean.
Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently, and appropriately.
Applying: Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately.
Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.
Engaging: Seeing mathematics as sensible, useful, and doable—if you work at it—and being willing to do the work.
A simple way to carry out these five tasks in a university course:
(I) Reading the textbook, (II) Working through examples, (III) Struggling through practice problems, (IV) Discussing difficulties with professors and other students, (V) Understanding and building on what was accomplished, and (VI) Repeating this process consistently.
b. For each of the steps listed above, consider the method of René Descartes:
Never accept anything as true unless it is clearly known to be such.
Divide difficult problems into as many parts as possible.
Proceed from the simplest problems to the more complex.
Make the connection complete and general so that nothing has been overlooked.
Benefits of Mathematical Reasoning:
Improved Problem Identification (Identifying which path to take, i.e. asking the right questions)
Improved Analytical/Logical Reasoning (Proceeding along a path, i.e. using problem-solving methods)
Improved Solution Justification (Recognizing when the end of a path is reached, i.e. providing robust and stable solutions)
The Golden Ratio and Golden Spiral
Basis Selection from Sparse Data
Initial Condition Scaling of 2D Kuramoto-Sivashinsky Time-Dependent Solution on a Rectangular Domain
Domain Scaling of 2D Kuramoto-Sivashinsky Time-Dependent Solution on a Rectangular Domain
Finite Element Simulation of Chaotic Dynamics in 1D Kuramoto-Sivashinsky Equation (160 grid points)