Working my way through college by tutoring as many as 6 students per week, I graduated summa cum laude with honors in mathematics from GSU and earned an MS in mathematics from UCI.
Working as a pension consultant and ultimately as Director of Actuarial Consulting taught me to effectively present complex issues in understandable terms to CEOâ€™s.
In my second career as a high and middle school math teacher I taught all math courses from fractions through calculus, developed courses in math h...
Linear algebra is the study of simultaneous linear equations. They can be solved with one of two methods: substitution or elimination of a variable. With two equations in 2 unknowns they both have their advantages. However, with a 3x3 or higher system elimination becomes much more powerful and lends itself to computer solutions. A simple linear equation looks like: ax=b. A system of linear equations using arrays of numbers (or matrices) can be written as AX=B, and it begins to look like simple algebra all over again as long as there exists an inverse matrix of A that can be applied to solve the equation for the vector X.
Linear equations can be used to approximate more complicated systems. As an actuary we used a 6x6 array to approximate complicated calculations of Social Security benefits to speed up computer calculations of pension benefits payable over the working lifetime of participants in pension plans.
I took linear algebra as an undergraduate at Georgia State University. In graduate school at University of California at Irvine I worked with Dr. Howard Tucker and got a Masters degree in Statistics. Dr. Tucker's approach was to define statistical tests in matrix notation. Using this approach we could derive all of the various common statistical tests as well as define new tests using diagonal matrices that could be n by m. In essence we would design multidimensional ellipsoids (the extension of the one dimensional confidence intervals to test hypotheses with n variables. This work was applicable to the medical school and biological sciences which we invited in each week to design tests for their experiments. Needless to say we had to be very familiar with linear algebra and triangularization of matrices and linear algebra.
As a high school teacher I taught students in algebra 2 how to solve simultaneous systems of equations using substitution, elimination and matrix calculations on TI calculators.
One of my teachers of graduate probability at UCI was Ed Thorpe, who wrote the book on how to beat Las Vegas at blackjack. Hopefully your teacher will be clearer than he was.
Probability is the mathematics of chance. Theoretical probabilities are based on a ratio of the number of ways a certain event can occur to the number of ways anything could happen. Therefore counting is very important. It starts with the fundamental theorem of counting: if there are n ways of getting A and m ways of getting B, then there are n x m ways of A and then B. Counting progresses with the useful ideas of permutations (for ordered sets) and combinations (for sets without order). Using counting and simple probability facts students will learn of the Binomial Distribution and the Law of Large Numbers will lead to the "Bell Curve". The whole subject of Probability was started in a series of letters between Pascal and Fermat who were discussing the likelihood of winning a game that was prematurely stopped and the players wanted to distribute the pot based on the likelihood of ultimately winning had they been able to continue the game. Today the course is usually taught as Probability and Statistics or just as Statistics. Probability has found its way into all the sciences including the daily weather reports, biology and even theoretical physics, and that is why you need to know about it.
Probability is the mathematical study of the likelihood of events when the population is understood. Statistics is the mathematics of making inferences about a population that is not understood based on a random sample from the population. In probability we try to deduce from what we know; in statistics we try to infer things about what we don't know. Important concepts include measures of the sample data's center (mean and median) and the extent of its spread(standard deviation). The law of large numbers can be used to approximate these unknown values within a range with a degree of confidence measured by the probability that the values lie within the range. There are various statistics that can be used to test the validity of a hypothesis. Some of the formulas are intimidating and your answers will sound something like "I don't know what the mean is but I don't reject what we have assumed the mean to be and I will probably be right in that assumption 95% of the time." Yea,...your going to need a tutor!