- Introductory statistics -
19 May 2011
Mathematics is fundamental in the study of life and nature and thus one of the essential tools to understand events in our life and universe. Based on Logic or proper and acceptable reasoning, Set theory, Number system, Algebra, and space (geometry) study high school Math is supposed to provide the students adequate basic foundation for the further study or required entry level skills to enter real life work place.
By studying the basic Mathematics students will also become well rounded persons, good citizens of the world and our future life model, be reasonable, be open to many other different ways of seeing and understanding the events, and open to further discovery and findings. The study will also help improve your
mind and brain work in intuitive and logic-based processes and at the same time instill the love for more discovery.
Some of the problem solving skills developed in the study of Math 11, 12 and junior college include:
- Understanding the problem, given information, conditions or circumstances, and unknown information to be found
- Making reasonable assumptions, creating geometrical and algebraical representations of the problem statements
- Dividing the problems into smaller and easily solvable problems if necessary
- Creating additional constructions algebraically or geometrically to make progress in thinking
- Finding the relationships between informations (unknown and known informations)
- Recalling necessary theories, formulas, Mathematical properties, methods or techniques, past experiences, etc.
- Selection of suitable ways/methods and apply these to get to the solutions
- Inspecting the solutions to find if they are possible
- Recording for future use
You should give enough time and effort to understand the Mathematical ways of seeing the events, and to apply the techniques you learn in the real life situations to discover the beautiful solutions. Some of these solutions will become amazing new methods for further problem solving.
Students read the books, listen to the lectures, take part in the discussions and practice solving problems. Many students make two kinds of records.
(1) Important notes, theories, properties and formulas
(2) Work solutions
Students practice the art of
- understanding the problems
- creating diagrams to assist in imagining what events take place in the problem
- transforming the textual information into mathematical expressions whenever necessary
- finding the relationship between unknown information and known information
- with the use of record (1) above plus past experiences, choosing the methods or formula to tackle the problem
- solving for the solution and checking their validity
Starting from what is given students move to next steps in the process. Every time a new step is about to be made there must be a reason: why you do this next statement? Reasons must come from the Math you learn or they must be well accepted traditionally.
As in the study of Physics, proper & correct understanding of meanings and properties of elements of Mathematics is very important.
Take interest in Math. It is a beautiful wonder world.
- updated 05 September 2016 -
As usual I will focus on clear understanding of concepts and theorems, thinking with logical reasons. Then we will go on to understanding of the problems and , when necessary, translating the problems (textual statements) into Mathematical forms so we can use the Mathematical theories to find the possible solutions. Creating neat and proper diagrams, as well as strong foundation of basic Math will always be important.
My tutoring services are available for
- Precalculus 11 & 12, AP Calculus, IB Math
- Calculus I, II & III
- Linear algebra first course
- Introduction to ordinary differential equations
- Introduction to real analysis
- Introductory Statistics
Tutoring time: to be discussed to meet your convenience.
One on one fee: $ 30 per hour (minimum 2 hours per session)
If more than two hours, $ 25 per hour from the third hour.
We can study at Surrey city centre library, Guildford library, Fleet wood library, Newton library or University campus in these areas. I may also go other places depending on the schedule and travelling time.
- update on 31 Jan 2010 -
As usual one important thing where we will put good effort is to be able to understand and translate the real life problems into Mathematical expressions or models. The next steps will include finding appropriate theory or theories to find the solution(s) for the problems and checking whether they are possible. It is important to understand the theories and techniques of Mathematics and their limitations, assumptions and axioms on which they stand.
There are more on learning Mathematics. I will update this page later for further information.
If you want to take up one on one tutoring on Mathematics please drop me an email and I will reply to you.
Please include the grade or course you are studying at, your contact details and some information about the course outline. I will be more than happy to do my best in assisting you in the study of Mathematics.
External links (open in new window):
- GeoGebra Graphing and Algebra Dynamic online worksheet (hosted in my other web hosting)
- Metric and Determinant
- Mathematical constants (∏, e, etc.)