School math
Math 8, 9, 10, Precalculus 11, 12, Calculus 12
Algebra, Geometry, Trigonometry, Probability and stats
Computing in spread sheets (Libre office calc, Excel)
Computing, graphing, animation in Geogebra
Self study of math
Basic set theory & logic
University math & work
Calculus 1 and 2 (differential and integral), Calculus 3 (multivariate)
Introduction to ordinary differential equations (ODE)
First course in Linear Algebra
Introductory Statistics with probability
Math for jobs, projects or modeling
Writing math documents for some topics of interest and for self study
What do we think about math?
Mathematics is used in the study of life and nature and thus it is one of the essential knowledges to understand the events in our life and universe. It is a necessary tool in all branches of science (social, natural, applied). As math is expanding, it is also increasingly used in arts.
A static object such as a picture can be modelled in math. A dynamic event such as the rain fall can be modelled in math using natural science knowledge. An observed relationship between temperature, pressure and volume of a gas in a bottle can also be modelled in math using elements of science. These models are not exact and complete representations of what they are representing. However, they give us a view from which we can extract some knowledge that may be useful for decision making. A math model of a picture can tell us density and compositions of different colours at each region in the picture, Rain fall in math formula can be used to estimate the volume of water collected in a tank in an hour of rain.
In addition to ever widening range of applications, math is also a body of knowledge in its pure form. Our mathematical minds can explore physical and abstract objects and translate them into math with no intension of applications. Nevertheless, pure math theories can be used in applications.
Based on logical reasoning, set theory, number system, algebra, space (geometry), and our ability in modeling the events in math, school and college studies are designed to provide us a foundation needed either to enter the workforce as juniors or to continue further study in universities and other higher institutions.
Unlike our natural languages, the language of math is strong in consistency and precision. Also, math theories and associated rules of decision making are the same for everyone. It gives us a chance to increase honesty and reduce bias. By studying foundations of math (either at school or self study), we can become well rounded and responsible citizens of the world and its future. We can become more reasonable, open to many other different ways of seeing things and willing to understand the events, and open to further discovery and experiences. The study of math can also help improve our mind and brain work in life.
Some of the problem solving steps we learn:
Correctly writing the problem statement (likely progressively) out of known information of a situation. Inspection for errors, completeness and precision.
Understanding the problem statement correctly. Discover the scope of work, the objects we are dealing with and their possible values, known relationships. Explore the theories of math relevant to the problem. In case of insufficient knowledge, do some reasonable assumptions and declare them. What will be form of solution ?
Dividing the problem into smaller and easily solvable parts if necessary and when possible.
Find a procedure to solution. Without a procedure, we decide on what is next step along the way. Whenever we find ourself in a hopeless state, we back track and find an alternative step.
Writing the found final results for inspection. Write the solution as complete and precise as possible. Record both successes and failures for future use.
Sufficient time and effort are necessary to understand the mathematical ways of seeing the events and do reasoning.
We discuss diverse topics in math. Some of them are listed below.
Basic set theory and propositional logic because the set notations are widely used in writing formal statements along with logic in building theories of math. Logic may be seen as a collection of rules of inference which are needed to construct math theories that are consistent and precise.
Construction and use of each component of math such as numbers and their properties, comparison and arithmetic operations, variables and possible values, graphs, relations and functions.
Idea behind mathematical objects such as trigonometric functions.
Making diagrams. Writing neat and clear, and as complete and precise as possible.
Making notes out of textbooks, important discoveries from practice works, and from our mistakes.
Improvement of our learning efficiency and skill in problem solving, modeling, translation between the views, making diagrams and statements.
Asking and answering questions are a big part of our study. By asking we can discover more about our math knowledge. We can find our weak points and short comings so that improvements can be done.
Available services:
Online tutoring.
In person tutoring if you can travel to where I can come.
Writing custom math lesson plans or any other documents.
Writing a set of sample solved problems with explanations.
Writing notes for a selected topics in math.
If you need something which is not in above list, please let me know and we can discuss.