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Algebra 1

Algebra introduces the concept of variables. Students of algebra apply previously learned rules like the distributive law and PEMDAS to expressions and equations which now include variables. In addition, they learn rules like the addition principle of equality and the multiplication principle of equality. The goal is to manipulate the equation so a value of the variable can be calculated. Sorting out all these rules and deciding what should be done next can be confusing. I have taught classes...
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Algebra 2

Algebra 2 is a continuation of algebra 1. In algebra 2 students are introduced to polynomials. The rules for basic arithmetic operations on polynomials (addition, subtraction, multiplication, division and exponentiation) are examined. Rational expressions (quotients of two polynomials) are studied along with the rules for basic arithmetic operations on rational expression. At the core of rational expressions is factorization. I simplify the learning of these concepts by showing how easy they can...
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Calculus

Calculus is the mathematical study of change. It has two branches. Differential calculus is the branch of calculus focusing on rates of change; for example, the slopes of curves and surfaces. Integral calculus is the branch of calculus focusing on accumulations; for example, areas under curves and volumes enclosed by surfaces. The two branches are connected by the Fundamental Theorem of Calculus discovered independently by Isaac Newton and Gottfried Leibnitz. My first exposure to calculus was...
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Physics

Physics has been described as the science of “why things work.” Physics deals with such things as mechanics (force, energy, motion), sound, heat, light, electricity, magnetism and atomic structure. My first exposure to physics was during high school. Receiving straight A's in physics as well as all my other high school science courses earned me a Proficiency in Science award at graduation. I continued my study of physics in college with the calculus-based three semester physics sequence required...
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Prealgebra

Prealgebra focuses primarily on arithmetic. The most fundamental skills are reading and writing of whole numbers. From there, basic arithmetic operations of addition, subtraction, multiplication and division are defined for the whole numbers. Wrapping up the study of arithmetic on whole numbers, exponentiation and order of operations (PEMDAS) are introduced. Knowing how to work with whole numbers well is the key to the bulk of a prealgebra course. The same skills (reading and writing, basic arithmetic...
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Precalculus

Precalculus explores topics that will be applied when a student studies calculus in the future. A strong mastery of precalculus will streamline a student's study of calculus. Conversely, having a weak background in precalculus makes the study of calculus more difficult since the student will feel he has an overwhelming amount of things to learn simultaneously. Precalculus involves memorization. For many students, it is the first math class they have taken where memorization plays such a profound...
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Trigonometry

Trigonometry has been largely replaced by Precalculus in many schools. Like Precalculus, trigonometry involves a lot of long term memorization. A trigonometry class focuses on the six fundamental trigonometric functions and the relationships between them. Students learn laws that allow them to solve triangles (determine angles and sides) for oblique (non-right) triangles. Trigonometry has many applications. The word problems in a trigonometry course challenge students by drawing from applications...
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Statistics

Statistics is the science of collecting, organizing, summarizing and analyzing information in order to draw conclusions. A typical statistics class begins with an overview of descriptive statistics. Descriptive statistics consists of organizing and summarizing the information collected. This is usually done through charts, graphs and tables as well as computing numerical summaries such as the mean and standard deviation. Most students have seen these types of summaries in the media and have no...
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Probability

The study of randomness is at the heart of probability. While individual occurrences for the outcome of a random event (e.g. the toss of a fair coin) are impossible to predict in advance, if repeated many times the sequence of outcomes will exhibit patterns. In probability, formulas are devised for the predicted of these patterns (e.g. 50% heads, 50% tails for a sequence of coin tosses). Probability forms the mathematical foundation in inferential statistics. It is traditionally placed in between...
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Study Skills

It is a natural reaction for today's over committed and over stressed students to object to the idea of having to make room in their busy schedules for time devoted to learning study skills. In reality, they can't afford not to spend the time necessary to learn these valuable skills. Mastering study skills results in the greatest academic success without undo stress. I am always learning. I have developed my own system of studying which stresses listening, note taking, organization, finding outside...
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Discrete Math

Discrete math is a catch-all term encompassing many diverse areas of mathematics. There is no universal agreement as to what constitutes discrete math. Discrete math is defined less by what topics are included than by what is excluded. Excluded are notions of continuity upon which calculus is built. Consequently, discrete math is described as "non-calculus" math. Finite math is an introductory course in discrete math. A typical finite math course is a survey course consisting of: linear functions,...
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Differential Equations

Differential equations are equations involving a function and one or more of its derivatives. Traditionally, they have frequently appeared in the mathematical models constructed by natural scientists and engineers. However, in recent times, their use by social scientists has increased dramatically. This is especially true in the area of economics. Only the simplest differential equations admit solutions given by explicit formulas. Beyond this, numerical methods using computers are called upon...
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C++

C++ is one of the most popular programming languages. The language was developed by Bjarne Stroustrup as an enhancement to the C language. Consequently, C++ inherits most of C's syntax. C++ added classes, virtual functions, operator overloading, multiple-inheritance, templates and exception handling among other features.

It is a multi-paradigm language enabling programmers to blend functional, generic, modular, procedural and object-oriented styles. I have several decades experience developing...
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Biostatistics

Biostatistics is the application of statistics to biology. It typically involves the design of a biological experiment from which data is gathered. From that point, the tools of descriptive and inferential statistics are brought to bear. The data are first analyzed and second summarized by numbers, tables and graphs. Finally, inferences are drawn from the results. At the core of an introductory biostatistics class, are the principles and practices taught in the introductory statistics class I...
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C

The C computer language is one of the most popular computer languages of all time. C is a general-purpose computer language which is flexible enough for implementing system software (through its low level memory access capabilities) as well as portable application software. Long before multicore processors hit the consumer marketplace, I had been developing software for massively parallel computers with as many as 65,536 processors using C. I have several decades of software development experience...
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Computer Programming

Computer programming involves designing, writing, testing and refining source code. The purpose of computer programming is to build a set of instructions computers follow to accomplish various tasks such as numerical computation, information storage, information retrieval and display of images and information. I have almost four decades of computer programming experience. I have developed programs in Basic, Fortran, Pascal, C, C++ and Java. Most of these have involved engineering simulation. In...
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Fortran

I have extensive experience in computer programming. One programming language I specialize in is Fortran. The name Fortran comes from the phrase "formula translation". It is the programming language of choice for scientists and engineers. Most computer programmers are unfamiliar with Fortran. I wrote my first Fortran program in 1976. I have kept up with the changes to the language through Fortran 2008.

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Linear Algebra

Linear algebra is the study of sets of linear equations and their transformation properties. Combined with calculus, linear algebra allows the solution of systems of linear differential equations. Linear systems of equations arise in a diverse range of applications including agriculture, business, economics, finance, sociology, demography, political science, biology, chemistry, ecology, genetics, astronomy, electronics, engineering and physics. For this reason, linear algebra is often viewed as...
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Pascal

Pascal is a computer language designed from scratch by Professor Niklaus Wirth in the 1960s and implemented in 1970. Pascal was originally targeted towards academia. The objective was the teaching of good programming style. It embraced structured programming and stepwise refinement (top-down programming design). The original Macintosh OS was written in Pascal. Like many Fortran programmers of the 1980s, Pascal captured my interest because it was a way to transfer engineering simulation programs...
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UNIX

In the early days of computing, operating systems were vendor specific. They also were oriented towards single task batch computing. Unix was developed at AT&T Bell Labs to be portable, multi-tasking and multi-user in a time-sharing environment. Over time, Unix developed various vendor-specific flavors. Over the course of fifteen years, I gained significant experience developing software for Sun (Solaris), Hewlett Packard (HPUX), and Silicon Graphics (IRIX) workstations. In addition to developing...
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Visual Basic

I took my first class in Basic in 1977. Back then, in keeping with the acronym Beginners All Purpose Symbolic Instruction Code, it was simple, small and uncomplicated. My first internship was to maintain and extend a Basic computer program designed to calculate pressures and flows in a piping network. Over the years, the art of computer programming evolved. Unlike many early computer languages, Basic has continued to be relevant. This is due, to a large extent, to Microsoft and its Visual Basic...
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Mechanical Engineering

I graduated from Northwestern University in 1990 with a doctorate in Theoretical and Applied Mechanics. Applied mechanics bridges the gap between physical theory and its application to technology. It is fundamental to many branches of engineering, especially mechanical and civil engineering. In these disciplines it is commonly referred to as engineering mechanics. Engineering mechanics can be subdivided into statics, dynamics, mechanics of materials, fluid mechanics and continuum mechanics. I...
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Civil Engineering

I graduated from Illinois Institute of Technology in 1981 with a bachelor's degree in Civil Engineering. I have worked in the water distribution department for the City of Chicago, a piping stress analyst for the nuclear industry and engineering simulation software developer for a national laboratory.

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ACT Math

The ACT Math exam measures mathematical skills students typically learn through the end of 11th grade. Most students preparing to take the ACT need a review of math skills they may have learned but have since forgotten. They also need help in the judicious use of calculators on the ACT. My ACT Math score placed me in the 95th percentile nationally. I have helped students improve their standardized test scores for undergraduate (ACT and SAT), graduate (GRE and GMAT)admissions. I use a combination...
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ACT Science

Preparing for the ACT science does not involve memorizing science facts. Rather, it should focus on reading graphs, tables and research summaries as well as looking for patterns in numbers. Test objectives include measuring a student's ability in extracting information as well as making inferences. My ACT Science score placed me in the 98th percentile nationally. I have helped students improve their standardized test scores for undergraduate (ACT and SAT), graduate (GRE and GMAT)admissions. I...
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