Algebra problems to get you thinking

My 8 year old son wanted to learn calculus the other day.  So, I thought he should study a little algebra first.  Here are a series of problems that are similar to the ones that I gave him:

x-5 = 10

He had no problem with that one

2X = 10

He thought that X needed to be a digit in a number that started with 2.  After I explained that it really was 2 times x = 10, he was able to figure it out.

Then combining the two operations:

2x -5 = 15

No problem with that one.

x^2 = 9

Needed a review on squares.  We only covered the positive answer to this problem.  I have not gotten into negative numbers with him yet.

x^2 + 4 = 20

This is the one that we are currently stuck on. 

Do you have suggestions on how to teach an eight year old algebra and calculus?  Leave them in the comments below. 

MSAM: Successful first semester

I just completed my first semester the Masters in Applied Mathematics program at the University of Houston.  I had to take an undergraduate class that was required for the graduate classes I need to take.

“Advance Multi-variable Calculus” by Dr. G. G. Johnson was a very good class that filled in many of the whole that I had in my understanding of calculus and the techniques behind mathematical proofs.  It had a different format than the lecture/exam types of class that have been the standard class structure.  It is easy in those lecture/exam classes to go through the entire the class without actually having to think or learn.  This class was taught in a “give problem”/”work problem”/”defend solution” method.  There were only 3 or 4 days of lectures.  The rest of the time was spent with students at the board working problems with the professor and the other students asking questions.  This ensured that there was no “weakness” in the student’s understanding of the problem and the solution.  The only downside were the days that students were at the board that did not really understand the solution or sometimes, even the problem.

Anyway, I have to report that this first class turned out very successful!

Next semester, I am considering taking a class on the math behind options:



Math 3334: Class Notes

Def 7 Suppose M is a point collection. The statement taht P is a boundary point of M means P is a point and R is a region containing P, then R contains a point of M and a point not in M.

Prob 5 No point of a region is a boundary point.

Prob 6 Every region has a boundary point.

Prob 7 If P is a limit point of the point set M must P belong to M?

1) S1 and S2 are subsets of numbers.

2)  S1 and S2 have no number in common.

3) Each point in S1 is to the left of each point in S2.

4)The union of S1 and S2 is the real numbers R.

5) Either S1 has a right most number or S2 has a left most number.

Prob 8 There is a positive number t such that t*t=3.

Prob 9 If M is a number collection and B is a number such that each number in M is less than B than there is a number L such that no number in M exceeds L and if a is a number less than L, than there is a number in M greater than a.

Def 8 The statement that t is a graph means G is a point collection.

Def 9 The statement that f is a function meeans f is a graph such that no two points of f has the same first number.

A boy genius who played his numbers just right – National –

A boy genius who played his numbers just right – National –

Math 3334: Class Notes

Definition 1 – The statement that P is a point means P is an ordered number pair.

Defintion 2 – The statement that Q is the plane means Q is the set of all points.

Definition 3 – Suppose each of x and y is a point. The statement that D is the distance between x and y means D= [(x1– y1)2 + (x2-y2)2]1/2 where X=(x1, x2) and Y=(y1, y2).

Definition 4 – The statement that R is a region means there is a positive number c and a point P and R is the set to which x belongs, only in the case x is a point and D(x,p) < c. We may denote such a region by Rc(P).

Problem 1 – if each of R and S isa region adn there is a point P common to R and S, then tehre is a region T such taht P is in T and every point of T is in each of R and S.

Definition 5 – Suppose M is a point collection. The statement that P is a limit point of M means P is a point and if R is a region containing P, then tehre is apoint of M, distance from P, that belongs to R.

Problem 2 – Every point of a region R is a limit point of the region R.

Problem 3 – If R is a region and P is a point not in R, then P is not a limit point of R.

Problem 4 – If M is a number collection that contains the number 1 and if n belongs to M, then n+1 belongs to M, does M contain all positive integers?

Definition 6 – The statement that M is an infitie point collection means if N is a positive integer then M has N points.