Hi, my name is Uran. I have taught at the university level on diverse topics such as Corporate Finance, Managerial Economics, Business Statistics, Introduction to Statistics, and Mathematical Statistics to graduate students who are not Statistics majors.
I have a Bachelor's degree in Electrical Engineering, an M.B.A., an A.B.D. in Finance, and a M.S. and Phd degree in Statistics. I also am currently pursuing a Computer Science degree. Hopefully, I will be done soon. I have tutored...
Hi, my name is Uran. I have taught at the university level on diverse topics such as Corporate Finance, Managerial Economics, Business Statistics, Introduction to Statistics, and Mathematical Statistics to graduate students who are not Statistics majors.
I have a Bachelor's degree in Electrical Engineering, an M.B.A., an A.B.D. in Finance, and a M.S. and Phd degree in Statistics. I also am currently pursuing a Computer Science degree. Hopefully, I will be done soon. I have tutored mathematics, statistics and
probability, electronics, financial accounting and ethics for student solutions nearby California State University at Northridge, and another tutoring organization near Oregon State University at Corvallis. I tutored for Equal Education Opportunity program
at Oregon State University as well. Sometimes, I have to work with math-challenged students or students with learning disability (such as aural or visual dyslexia). I am generally very patient. I do not get frustrated. I break down each concept into easier-to-understand
component steps. I try to use visual or symbolic approaches if more conventional approaches fail. Analogies can also be helpful. Following are two examples of my teaching style on two sets of concepts: Example 1: Suppose a student is trying to solve the following
hypothetical problem. Suppose x + 3 > 4 is the proposition. Student is tasked to identify the range of values of x that satisfy the above inequality. Since x can stand for any real number, we can try to let x = 0 and see if 0 + 3 > 4 is true. It is not, and
therefore the mathematical sentence x + 3 > 4 would not allow x to take on the value 0. 0 is out of our consideration. If x is even less than 0, then since x < 0, x + 3 < 0 + 3 (since x started out to be less than 0, three greater than x is going to be less
than 3 greater than 0, or x + 3 < 0 + 3 = 3). If x + 3 < 3, then it cannot be greater than 4, and therefore, any number less than 0 is also not going to be such that x + 3 > 4. So, we can throw out all the choices for x that are less than or equal to 0. Similarly,
let x = 1. 1 + 3 > 4 is also false. By similar argument, any choice of x that is less than 1 cannot be greater than 4 (See if student can reconstruct my argument). Be very patient and stress that he/she needs to connect the concepts step by step here. Somewhere
in the discourse, we might just have to remind him/her that the statement x + 3 > 4 is either true or false, there are no in-between's. However, as soon as x gets slightly above 1, x + 3 will be slightly above 4. So all x > 1 will satisfy the above statement:
x + 3 > 4. This then suggests a method to deal with these "single-inequality" type of problems: Step 1) Treat inequality as if it were an equality and solve the equation for x. x + 3 > 4 is written as if it were x + 3 = 4. x + 3 - 3 = x = 4 - 3 = 1. Step 2)
The answer is the number that divides the region for x that makes the inequality valid and invalid. See if number smaller than the answer from Step 1 is valid: x a little less than 1 makes x + 3 a little less than 4. Therefore, any number less than 1 would
make x + 3 > 4 untrue. x a little greater than 1 makes x + 3 a little more than 4. Therefore, any number greater than 1 would make x + 3 > 4 true. And we have the solution: {x: x > 1} satisifies the inequality x + 3 > 4. I would go through these steps and
offer explanation and how each step is motivated, to help students understand their subjects. Illiciting feedback from the student at every step of the above long argument is important. If student does not understand any of the intervening steps, I would try
to explain the concept one more time, using the old approach. If not, then a new approach will need to be designed, sometimes even on the spot, to accomodate student's understanding. If after a reasonable number of tries, the student still does not get it.
We may skip to another topic and try later. Beating a point to death all at once does not help student's own self-image. Many often times, a student deals with a complex series of tasks and if we can supply them with basic set of numbers to let them go through
the calculations, it would make the entire problem structure more concrete. Sometimes, if algebraic symbolism fails, geometric pictures can help. In any case, example problems should be given to students that are congruent to the complexity (the degrees of
freedom) in the problem. For example, in net present value calculations in finance, there is a very simple formula connecting future values of a sum of money (how much a sum of money will be worth) to the present value of that sum (the initial deposit). Briefly,
the future value = present value* (1 + interest rate)^number of compounding periods, with ^ standing for exponentiation. Then I can let students work through some of the following problems: i) if future value = 1000, interest rate is 9% per year, number of
compounding years = 2, what was the present value? ii) if present value = 1000, interest rate is 9% per year, number of compounding years = 2, what will be the future value? This enforces the idea that with positive interest rate, future values will be greater
than present values. Future bank balances will be greater than present bank balances if depositors do not withdraw their money. iii) if future value = 1500, present value = 1000, number of compounding years = 6, what was the interest rate? iv) if future value
= 1500, present value = 1000, interest rate = 9% per annum, what would be the number of compounding years. Now, I give the grand summary of all these types of problems. There are four variables, present value, interest rate, number of compounding periods,
future value. Given three of the four as numbers, and because I have one equation relating them: future value = present value*(1 + interest rate)^number of compounding periods, I can solve for the value of the other variable. Other financial formulas, such
as bond pricing, annuity pricing follow the same structure. Only that the number of variables are different.