Edward is approved to conduct lessons through Wyzant Online. Wyzant Online allows students and tutors to work remotely via video, audio, and collaborative whiteboard tools. For more information about how online tutoring works, check out Wyzant Online.
If you’re interested in online lessons, message Edward to get started.
Illinois Institute Of Technology (Engineering)
Illinois Institute Of Technology (Master's)
Northwestern University (PhD)
I have mastered skills in many diverse areas. Determination, confidence, and knowing how to study have been the keys to my success. I focus on helping my students build these fundamental attributes in addition to learning the subject.
After 14 years in government-sponsored research, I turned to education out of the desire to work in a more people-centric field. I have been an adjunct math instructor at Harper College for the past nine years. I have taught math courses to students of all ages, backgrounds and abilities. I have taught all courses currently offered by Harper college from developmental math through business calculus.
I have seven years experience tutoring students. My goals are to help my students learn the subject and become better learners. I believe many students have difficulty because they get lost in the details. My approach is to explain each step in the context of the total problem being solved. The goal is for students to see how each step contributes to answering the questions posed. My students see dramatic improvements in grades and test scores after working with me for only a few sessions.
I employ both traditional and modern tutoring techniques. Often I use web-based software for skill building. This is very effective for students preparing for standardized exams. The software identifies student strengths and weaknesses, and serves as a guide for the tutoring effort.
I enjoy hearing from former students. Many of them continue to work with me in subsequent classes. Seeing them fulfill their dreams is my greatest reward! I have mastered skills in many diverse areas. Determination, confidence, and knowing how to study have been the keys to my success. I focus on helping my students build these fundamental attributes in addition to learning the subject.
After 14 years in government-sponsored research, I turned to education out of the desire to work in a
Group rates: Parents always welcome (no extra charge). 2 students (same subject) - $40/hr per student. 3-4 students (same subject) - $30/hr per student. Larger groups - email me for details.
Edward is approved to conduct lessons through Wyzant Online. Wyzant Online allows students and tutors to work remotely via video, audio, and collaborative whiteboard tools. For more information about how online tutoring works, check out Wyzant Online.
If you’re interested in online lessons, message Edward to get started.
We are very pleased with Edward. He's very flexible and knowledgeable. My son is very receptive to his tutoring style. Thank you for helping my son on such short notice.
He helped with many subjects and topics that were unclear and explained them in a way to understand. Excellent!! He was patient and let the student ask many questions.
Ed does a terrific job explaining the concepts and showing you how to do the work. It really is a pleasure working with him. He is one of the best choices you could make when selecting a tutor. He really will help get you on track and improve your grades. This is your guy!
He is a very helpful and good tutor. We solved several problems and I learned important tips. Edward explains everything and I learned things I didn't know about.
Edward does an amazing job. He is very patient and does a great job of explaining complex concepts. He is flexible with his schedule and is very knowledgeable about the subject.
We retained Edward for ACT math section strategies and preparation. Ed is very knowledgeable about math disciplines. He was reliable, patient and attentive. My daughter was looking more specifically for guidance on ACT/SAT testing strategies rather than mentoring on math concepts. We would definitely use him for academic tutoring if she were to struggle with advanced math courses.
I came to Ed for tutoring in a challenging grad-level engineering class. Ed was extremely helpful with strengthening my mathematics skills and has helped me turn my grade around to an A.
He really knows how to connect with the kids. This is our second kid using him. This first got into a top tier school due to his help.
He thought my daughter physics, and he went over all my daughter's physics problems. I recommend him since he is very patient with students and answer their questions with details.
My son's grade increased by a whole letter with only four sessions with Edward. Edward quickly understood my son's gaps in learning and addressed them!
Ed has been a wonderful tutor to my sophomore son this year. I originally sought out Ed to help my son with math (pre-calculus) but when I realized my son also needed help with Chemistry, Ed was open to help in that area too! He prepped for sessions beforehand (on his own time) and came to each session ready to tutor on Chemistry topics. I love that he also has background in computer programming so if needed, he can tutor on that subject as well. My son has seen a dramatic improvement in his grades since he began seeing Ed, which has helped his overall confidence in his classes.
Ed has been a great resource for my daughter. She enjoys working with Ed and he has helped her improve her calculus skills in a very kind, patient and gentle way. He is very personable and flexible and always tries to get the best out of her in every session. I recommend you contact Ed if you are looking for a calculus tutor.
Edward has tutored our son with college engineering classes. It is hard to find someone with the knowledge and expertise to tutor higher level engineering subjects. Edward has been of great help and our son got a 92% on his last test!! Thanks!!
It was such a pleasure to have professor ed he was very kind and just a wonderful person thank you so much I had a great tutor.
I would highly recommend him to any one
Cancelled on short notice and told to find someone else. I had test coming up so needed help. So better find someone else.
Edward was well-prepared for lesson and had a very good knowledge of the subject, which helped my confidence level in dealing with a subject (math) that I am timid about.
His teaching methods are very helpful. He walks through the problems and then has me try some on my own. He is very patient and doesn't mind re-explaining things and explaining them in a different way if you are having trouble understanding something. He is a great tutor overall!
Thank you Ed for helping me attain my goals in school and for being so nice about it! Ed is patient, kind and accommodating. He is responsible and knows what he is doing. Anyone would be lucky to have Ed for their tutor!
Java is required for my master degree program and the course materials and instruction are inadequate for me to actually learn the subject. The course had no pre-reqs and I've never, in a very long and successful academic career, consulted a tutor. Ed has been very helpful in explaining how constructors, methods, loops, arraylists, and hashmaps work together and I'm finally getting to the point where I don't just throw up my hands in defeat when I can't get something to work. Last night, I had a "eureka" moment while we were working through one of my assignments and we couldn't get it to pass through the instructor-supplied testing program. He watched me talk through the logic and try about a half a dozen things. Then I took a step back, said I think we're over-complicating things, looked at his solution, which was simpler than mine, but wouldn't fulfill the assignment's requirements of setting limits on the returns, and wrote a different sort of loop that worked. Best of all, I understood why it worked! Ed has been very patient with me as I throw spaghetti at a wall to see what works and talk through code to learn how it works. I'd recommend him to a student at any learning level who really wants to learn.
Ed helped me through Java and C programming assignments in my computer science program. He not only helped when I was stuck or had a specific problem, but he also taught me how to put to use the topics rolling around in my head, and how they interact with one another. For example, I understood for loops, and I understood arrays, but it wasn't until I was with Ed where I fully understood how a for loop could seed an array with elements (from a text file for example). He helped me tie together a bunch of different concepts and understand how they can and should interact with one another to solve a problem. From seeing how he approached things, I became better at being able to think like a programmer should, and I was much better at logically and syntactically working through a solving a problem than I used to be. It's obvious he knows a lot about math and computer science, so I would recommend him for either of those. He'll also try to help outside of tutoring hours to make sure you are successful. He will usually respond pretty fast to communication and is flexible with your schedule. What I have learned from him has definitely impacted my overall understanding and therefore grades, so if you're serious about your field and having some problems, you should not hesitate to contact Ed for help.
My daughter the student, came home ready for more! A great start! Calculus has dominated her college fun.
This will help it get easier.
In a short period of time, Ed helped my high schooler get caught up on AP Statistics. This was crucial to my child's success in school after having missed a lot of instruction time due to illness. He is patient and knowledgeable and knows how to adjust his teaching method to the student's learning style. Ed even ordered the books my child had in school in order to prepare the lessons, and continued with great success to provide online instruction when she was not available to meet in person.
Edward has been a huge help to my son as he embarks on this semester's Calculus journey. He has been prepared for each session and my son has been prepared for his daily class at school.
Ed is a straightforward teacher and only teaches things he feels you really need to know for your class. All my classes with Ed were informative and helped me learn the material faster and better.
Ed was a very good tutor and provided my daughter with more confidence/understanding than she had at the start of her tutoring sessions.
Ed has now tutored my son for over a year. It can be difficult if the student is reluctant to work with a tutor, but Ed has made it incredibly easy and pleasant for all involved. My son has always had a positive reaction to working with Ed and it helps his confidence immensely to be able to ask any question in a safe an nonjudgemental environment. Ed has tutored my son in AP Statistics, AP Physics, and Pre-Calc. Ed is professional, prompt, and flexible. All in all, a great experience.
Our son is graduating with his Engineering degree next week. We didn't always think this day would come!
Two years ago he was struggling with a required engineering class. His classmates were dropping it and he wanted to also. With the cost of an extra semester (or year!) of college in mind, we decided to hire a tutor. That's when we found WyzAnt and Ed. Ed was able to pinpoint the problems right away and help him with just a few sessions. Our son went on to pass the class. Since it worked so well, he continued with Ed for the next two years, meeting with him for a few hours a week to go over homework and study for exams. Yesterday was his final session as he finishes up his finals and prepares for graduation.
Ed is an excellent tutor and mentor. He's very knowledgeable and always prepared for the session (he asks for homework prior to session so he can review it). He's also very patient, friendly, and easy to reach. We're so glad that we found him!
Thank you Ed!
Edward was very patient and extremely helpful in assisting me prepare for the Illinois Test of Academic Proficiency (TAP). This test is statistically difficult to pass, and I was successful with the math tutoring from Edward. He came prepared for each lesson and provided with me with additional resources. Young or old, I would highly recommend his services!
I was taking calculus II and failing miserably! Ed helped me get through calculus II and pass with a B!! Ed joined me a long through my journey for calculus III and succeeded extremely well!! With his help I gained confidence and started to participate more in class! Ed is very patient and is the best!!
Ed was very patient and knew the subject well, I got help primarily with Calc 3 and Physics. He answered all my questions very well and did a great job of explaining it in a way I would understand. I am very grateful for Ed's help. I would definitely recommend him to my friends.
Just wanted to leave this note about Ed. He is working with my daughter who struggles with ADHD, so learning is not easy for her. Although she will never excel in Math, I believe Ed is a great tutor and has helped with her insecurities about learning.
Ed has not only worked hard with her, but has provided guidance for me to follow up with her tutoring to help make her successful in this college level math class. Although she is returning to school to complete the class, he has provided me with advice to continue and reinforce her learning.
Many thanks to Ed, for his time with my daughter and sharing his teaching skills. His genuine concern for my daughter's success is evident.
I am in grad school, and I never thought I would be expected to learn programming (Visual Basic) to support my degree. Technology is wonderful, but I felt overwhelmed. I contacted Edward through WyzAnt, and I am so glad I did. A couple of days before we met for my first tutoring session with Edward, I emailed him my syllabus and the appropriate version of Visual Basic. He downloaded the appropriate information to his laptop, and reviewed the instructions beforehand. At the appointed time, he was ready to proceed, and all I needed to do was turn on my laptop and allow him to instruct me in the appropriate steps to take in programming. In just one session of 75 minutes, I was able to submit my first project before its due date.
My daughter contracted a virus and strep throat during our planned tutor session time lines. Edward was very flexible and understanding. He also did a great job evaluating where my daughter was in the process of her subject ( math ), and then adapted to her need right before mid term finals. Nice job!
Math has always been a subject I've struggled in, when I began with Ed I still had trouble just adding and subtracting fractions. I met with Ed once a week, setting up sessions was very easy with him. Ed's schedule was generally flexible, which was great for me because I also work a part time job, as well as take classes. Ed was very patient with me, if we had a week or two of sticking with a difficult subject, for example: Rate problems, Ed would explain different ways to view the problem and a few methods on how to go about solving the problem. My original plan was to simply place into Math 101 on the placement test at my community college get my degree and be done with math forever. After studying with Ed, I took my placement test, and not only did I place into 101 but 140, 132, and 220! Without Ed's help I don't know if I would have had the patience to continue studying. His kindness, patience, and explanations were very clear. Ed actually reestablished my interest in math again. I know that the skills I have learned from meeting with Ed I will continue to put to use now and years to come in my education.
This is my first experience with an individual tutor. The time went by fast with the material we covered. It was like spending time with my instructor.
My tutor, Ed was very approachable and helped break down the statistical methods so that I could understand them. His meeting times were always flexible to my schedule and he was always prompt. He was always easy to reach either by phone or e-mail and he was always prepared for our lessons. Without his assistance I would have never made it through my college level stats class. Thank you Ed!
In most cases, tutors gain approval in a subject by passing a proficiency exam. For some subject areas, like music and art, tutors submit written requests to demonstrate their proficiency to potential students. If a tutor is interested but not yet approved in a subject, the subject will appear in non-bold font. Tutors need to be approved in a subject prior to beginning lessons.
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 of one-on-one coaching, test preparation websites and practice exam books.
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 use a combination of one-on-one coaching, test preparation websites and practice exam books.
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 in Algebra 1 as well as tutored the subject to students of all ages, backgrounds and abilities. I strive to cut through the confusion by introducing structure to the process and having my students view it from the perspective of "isolate and normalize" the variable. I also am effective at helping students struggling with word problems by stressing the concepts of identifying keywords and drawing diagrams. Later in an Algebra I course, equations and expressions with two variables are introduced. There, problems can be solved using multiple techniques (e.g. algebraic, geometric and numeric). Each student learns math differently, I strive to continuously adapt my tutoring style to each student's learning style.
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 be if students factor the polynomials and look for opportunities to cancel terms before multiplying or dividing. Often times, this requires addressing student weaknesses in factorization. Algebra 2 also covers quadratic functions in detail. Students learn multiple ways for finding roots of quadratics. Finally, algebra 2 typically ends with complex numbers, logarithmic and exponential functions. When I teach and tutor algebra 2, I stress mathematical reasoning and multiple approaches (algebraic, geometric and numeric). For example, many students are unaware that arithmetic on complex numbers can be done on the TI83/84 calculator. Teaching them this skill gives them a way to check answers.
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 have taught. I have experience helping bright undergraduate and graduate biology students get over the math hurdle they face when they take this course.
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 using the C programming language. In addition, I taught a class called "Introduction to the C Programming Language" at Daley College, one of the City Colleges of Chicago, for several years.
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 engineering simulation software during which time I have used each of the above programming styles. Long before shuttered glasses and 3D televisions became mainstream, I was developing C++ software for the 3D visualization of engineering simulations using shuttered glasses for specialized graphics devices such as the CAVE.
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 in high school. I was fortunate enough to have had a teacher who was a true scholar. He placed equal emphasis on having his students understand the principles and theorems as he did on having his students master procedures. Consequently, I started the undergraduate calculus sequence with a significant advantage over my classmates. I completed the entire undergraduate calculus sequence through differential equations with straight A's.
I have taught business calculus at Harper College. I have tutored high school students (honors and AP) as well as college students. My tutoring approach is to solve problems alongside my students and supplement what they are learning in the classroom (hows) with simple examples and sketches illustrating the underlying principles (whys). I believe students will apply the rules of calculus confidently and correctly after they develop an intuition for the underlying principles.
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.
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 addition, I have used both low-level graphics libraries such as OpenGL and high level graphics libraries like vtk to display the results of engineering simulations. I have experience developing user interfaces in Visual Basic and Java swing. I have developed shell scripts in Perl. I can help you in crafting new programs as well as deciphering the inner workings of legacy code. I have experience developing programs under a variety of paradigms (e.g. structured programming, object based programming and object oriented programming) as well as target platforms ranging from desktop PC to networked workstations ans supercomputers.
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 to approximately solve differential equations. Determining the explicit formulas for exact solutions to basic differential equations is covered in the traditional "diffy q" class at the end of the undergraduate calculus course sequence. My experience encompasses both the classical methods of solving differential equations taught in the traditional undergraduate "diffy q" course required for an engineering or science undergraduate degree as well as over two decades of experience solving systems of partial differential equations numerically on computers. I have completed graduate coursework on numerical methods such as the finite difference and finite element method for the solution of differential equations. In addition, my PhD thesis discussed solving the system of partial differential equations arising from structural dynamics on high performance parallel computer architectures using software I had developed.
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, matrices, linear inequalities, linear programming, the Simplex Method, counting (combinatorics), and probability. I have taught finite math within the university and community college setting for the past nine years. I am aware of the errors most frequently made by students. I diligently will point these out to you and make sure you won't fall into these traps when the exam comes around.
Finite math is an introductory course in discrete math. A typical finite math course is a survey course consisting of: linear functions, matrices, linear inequalities, linear programming, the Simplex Method, counting (combinatorics), and probability. I have taught finite math within the university and community college setting for the past nine years. I am aware of the errors most frequently made by students. I diligently will point these out to you and make sure you won't fall into these traps when the exam comes around.
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.
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 the work horse of modern applied mathematics. Linear algebra employs matrices as a tool for representing systems of equations. It goes further by establishing efficient methodologies for solving systems of equations which can be done by hand using pencil and paper (for small systems) or which can be readily automated and executed on computers and calculators. The main objective is finding values of variables satisfying all equations in the system.
I have studied linear algebra from both a pure and applied perspective. I have extensive experience developing computer programs for Gaussian decomposition, LU decomposition and eigenvectors. I have experience helping students learn the basics of linear algebra and the matrix solution of systems of equations in College Algebra and Finite Mathematics courses I have taught. In addition, I have tutored engineering students and shown them how to apply what they had learned in their math classes to systems of equations representing electrical circuits and civil engineering structures. In both the classroom and tutoring settings, I have helped students learn how to apply the linear algebra capabilities built into the TI83 and TI84 calculators to solve systems of linear equations.
MATLAB® is a high-level language and interactive environment for numerical computation, visualization, and programming. A MATLAB user can analyze data, develop algorithms, and create models and applications much faster than he could using traditional programming languages, such as FORTRAN, C/C++ or Java. MATLAB is used by instructors in numerical methods courses as a way for students to learn and gain experience working with algorithms without having to overcome all the roadblocks that go along with implementing them in traditional programming languages. I have extensive experience programming numerical methods in a variety of traditional programming languages (BASIC, FORTRAN, PASCAL, C/C++ and Java). I have used MATLAB to develop several different types of neural networks. Since it is an interpreted command line language, the approach I use to teach students a MATLAB command is to use small examples where the result of every computation can be printed and examined. For a multistage algorithm, a small dataset is chosen where it is possible to print, examine and discuss the intermediate results.
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 have taken advanced courses in these areas as part of my graduate studies. In addition, my PhD thesis outlined the development of novel computational tools for engineering mechanics simulations on high performance parallel computer architectures.
Microsoft Access is a database management system from Microsoft. Access consists of a relational database, graphical user interface and software-development tools. Access is a member of the Microsoft Office suite of applications. Like other Microsoft Office applications, Access is supported by Visual Basic for Applications I have completed a college level computer science course in relational database design and querying databases using SQL. I have experience building databases for personal, business and hobby applications.
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 from expensive mainframes to minicomputers and desktop computers like the Macintosh 512K I had just purchased. I went on to develop several computer programs for the classes I took at Northwestern University on that computer. For me, Pascal provided a stepping stone, first to C and then later to C++, Java and object oriented programming.
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 for engineering majors. I received straight A's in those classes as well. My graduate work was in engineering mechanics. Engineering mechanics can be subdivided into statics, dynamics, mechanics of materials, fluid mechanics and continuum mechanics. I have taken advanced courses in these areas as part of my graduate studies. In addition, my PhD thesis outlined the development of novel computational tools for engineering mechanics simulations on high performance parallel computer architectures.
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 operations, exponentiation and PEMDAS) are introduced for fractions, mixed numbers and decimals. After these skills are mastered for all number types, they are brought to bear in solving problems involving ratios, proportions, percents, measurement and basic geometry. Signed numbers are introduced at the end. I have helped students of all ages, backgrounds and abilities with prealgebra. Among them, have been adults returning to school whose skills have gotten rusty through lack of use or who perhaps felt discouraged by previous bad experiences with math and have since avoided it.
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 role. The objective must be long-term memorization so that the definitions and skills learned can be recalled and applied throughout the student's study of calculus. My tutoring approach focuses on making sure a student learns the fundamentals and realizes how often the fundamentals appear in the solution of problems. I train students to break a problem into smaller problems. I have them repeat that process until each problem involves applying a single fact they have previously learned. Every time they encounter and apply a previously learned skill, they are memorizing it. Repetition is key to memorization.
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 descriptive and inferential statistics in an introductory statistics class. When teaching and tutoring probability, I try to tie back the theory to everyday random phenomena (e.g. coin tosses, playing cards, dice) which students can experiment with to see how formulas can be used to predict the outcomes they are observing. I also stress a visual (Venn diagram or tabular) depiction of sample spaces and outcomes which often can be used in lieu of formulas to compute probabilities.
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 problem interpreting, using and constructing them. The second phase of a statistics course (inferential statistics) is much more difficult for students. Inferential statistics uses methods that generalize results obtained from a sample to the population. When guiding students towards the solution of a problem in inferential statistics, I use a visual approach to diagram the interrelationship between sample and population. Specifically, that the sample being analyzed is one specific member of a much larger sampling distribution. I emphasize the central limit theorem and its ramifications on the shape of the distributions (population and sampling distribution) in the diagram. Finally, all numbers given in the problem are transferred to the appropriate locations on the diagram. By being able to visualize the underlying logic and reasoning behind inferential statistics, my students are able to comprehend inferential statistics, choose the correct test to apply in a given situation and interpret the results of the statistical tests they conduct confidently and correctly. I also teach my students how to use the built-in capabilities of the TI83/84 calculator to do statistics.
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 references and using homework as a tool for preparing for tests. Practice, drill, repeat has served me well both in learning new skills and maintaining my current skills. In addition, I am continually researching and testing the latest ideas for optimizing learning. I am a licensed SOAR Study Skills tutor. SOAR is a highly acclaimed study skills system. One school measured SOAR to be 98.7% effective in improving student performance. I have helped students of all ages backgrounds and abilities make studying more efficient.
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 such as navigation, surveying, constructing models of periodic behavior and simple harmonic motion. My tutoring approach focuses on making sure a student learns the fundamentals and realizes how often the fundamentals appear in the solution of problems. The first step in a trigonometry problem often involves looking at a problems and devising a strategy to solve it. I train students to start problems by trying to identify previously learned facts that could be brought to bear on its solution. Every time they encounter and apply a previously learned skill, they are memorizing it. Repetition is key to memorization.
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 programs in higher level languages such as FORTRAN, C and C++, I also developed utility shell programs. I also was responsible for systems administration of two Silicon Graphics workstations. While doing systems administration, I was responsible for hardware and software upgrades, backups and creating and maintaining user accounts.
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 product. Object-oriented and event-driven programming as well as many other developments in computer languages have been incorporated into Visual Basic. Visual Basic also has tight ties to Microsoft Office. This has transformed the language from something a "hobbyist" might use for toy applications to a language which can deliver full-fledged custom business applications. I have several decades of computer software experience and witnessed this evolution of the Basic language. I can help you untangle the features of the language and develop your software program whether it be a toy hobbyist application or a custom business application tied into Microsoft Office.