Systems of equations, inequalities, trigonometry, exponential functions, radical expressions, etc. provide the basis for a lot of advanced mathematics that is needed in advanced applications in college and beyond.
I honestly do believe that algebra 1 is one of the best investments in terms of time spent studying/reward for a high school student.
Sometimes students find it a little bit dry as there are many rules and techniques to remember. But, a good teacher can throw in there some interesting problems to spice things up a little. For example, students often wonder what is all the fuss about inequalities. But once presented with a real-life simple problem like the one below, they often realize that actually inequalities are a relevant tool.
"Suppose you need to paint your house. Company A offers to do the job for $1000 + $100/hour. Company B, instead, offers to do the job for $150/hour. Which company should you hire?"
To find an answer one assumes that n is the number of hours of work required to complete the painting job. Then we choose to hire Company A if 1000+100n < 150n or hire Company B otherwise. The simple inequality can be solved to yield that we should hire company A if n>20. So, if we believe that the full job requires more than 20 hours overall, we should hire company A.
There is a rich array of problems in algebra that have practical applications like the one I just described above. Some students like abstraction, others respond better to practical situations. I have enough experience with the subject to cater to both groups of students.
I have a PhD. in Statistics with a minor in Math and I have used Algebra 2 for many years at the highest levels and, therefore, I am very familiar with the topics and I can spot very quickly where students are having problems. I can also draw on my experience to come up with practical problems that show how powerful this tool is in real life. Often high school students are not ready to appreciate the value of what they are asked to learn without seeing it at work in some real life situation.
My teaching philosophy.
Algebra 2 is one of those topics a student cannot really live without. Nowadays, a modicum of math is required in almost all fields and Algebra 2 teaches skills that are useful for a lifetime. The most important skill is learning to translate a problem from words to a mathematical formula and being able to perform the algebraic manipulations to find a meaningful answer. I like to teach this. Once a student understands this point, he or she can easily find the motivation to study some extra hours.
I also try to convey to the students I have worked with that a strong familiarity with Algebra 2 concepts is a must for those planning to pursue scientific degrees in college and who will have to deal with calculus.
I have an undergraduate degree in Economics and Business.
I have worked in the financial industry for over 12 years covering many industries from mining to REITS to the healthcare and the banking industries.
I also passed FINRA series 86 and 87 (stock analyst). Currently, I have passed CFA level 1 and level 2 and I am a candidate for the final level 3.
An important part of my work requires me to analyze business models for companies, study potential mergers and acquisitions and/or leveraged buyouts so I am quite familiar with notions such as cost of capital, capital budgeting, tax issues involved in mergers, and financial accounting for investments.
Calculus is one of my favorite subjects to teach because it is a very powerful tool and it is simply amazing in how many ways it can be deployed in real-life applications.
I have a Ph.D. in Statistics (minor in Mathematics) and I have used calculus a lot in my line of work as a quantitative financial analyst. Actually, stochastic calculus, a special version of calculus where the functions are random entities, is one of my main job tools.
Whenever possible, I like to use Mathematica and use the software amazing graphics to explain certain concepts.
My motto is "If calculus ain't fun, it is not being taught properly!"
I have successfully completed 2 courses in Econometrics while an undergraduate, one basic and one advanced.
I have authored a book of problems in Econometrics with detailed solutions and
I have taught 2 graduate courses in linear models for non Stat-majors at the University of Minnesota.
I have passed graduate courses in linear models and categorical data analysis in graduate school.
In addition, I have worked as an econometrician for two years and I have used several relevant computer packages
I have worked in the hedge fund and investment banking business for almost 15 years.
In my role I have had to analyze and value companies over a wide array of industries and countries.
I can help you with most concepts and I can assist you in developing spreadsheet models ranging from simple DCFs to complex mergers and acquisition or private equity leverage buyouts.
I can also help you with topics in portfolio management and more, a field where my education as a statistician and my work in finance really come together.
I held Finra series 7, 63, 86 and 87.
I have passed CFA level 1 and 2 and I am currently registered to take the final level 3.
QUALIFICATIONS: Since I earned an advanced degree, I had to take the GRE Exam myself.
Therefore, I am aware of the nuances involved in taking this test. The format changed in 2011, but the skills required are essentially the same. I have also taken several Revised GRE Quantitative tests to familiarize myself with the subject.
WHY STUDENTS LOOK FOR MY HELP? Most students I worked with on this subject approached me to get some help with the Quantitative section of the test and very seldom with the GRE Math-Subject Test.
THE GOOD NEWS, THE BAD NEWS. The quantitative part of the General GRE is not particularly difficult and it does not test any special math knowledge. That is the good news. However, a student can miss several points by not being familiar with some useful "tricks." Since when applying to selective graduate programs any extra point counts, that is perhaps the bad news. So, I could say that my goal is to help a student minimize the loss of these points by making sure he or she has acquired the all-important skills.
- I like to begin with a set of general questions covering all areas to be tested in the GRE-Quantitative Sections. This allows me to identify students' strengths and weaknesses.
- Normally, I spend some extra time on problems related to the areas that revealed weaknesses.
- In all cases, I like to look at problems and solve them in more than one way.
Not all students are comfortable with the same approach and some approaches are faster than others for certain students.
For example, I insist for using the calculator as little as possible, if an answer is given as 5/8, say, and a student worked with the calculator to find 0.625, then she is forced to check that 5/8 is indeed 0.625. This is even more important if radicals are involved.
- Finally, I like for students to develop time managing skills. Bad time management often lead to stress or demoralized students and neither is good for overall performance during the test.
The GRE-Math Subject test is a very different "creature". Here one has to command a good understanding of several topics. It is definitely a more challenging quantitative task than the general part of the GRE. Essentially, one has to make his or her strong areas count as much as possible and try to improve in areas where knowledge is weak or spotty. Tutoring for the Math Subject test is not any different than tutoring calculus or algebra, say.
My main qualification to teach Italian is that I was born in Italy and it is therefore my native language. I completed high school and my undergraduate degree in Italy before coming to the US to pursue graduate school and eventually work.
Teaching a foreign language, in my opinion, has to be as much fun as possible. This does not mean that one can make the grammar part pure enjoyment, but the teaching should not become a pure sequence of chores either. Interspersing conversation and grammar is my favorite approach. To keep conversations simple, sometimes I employ the use of situations and roles (say, we are in the grocery store, where I ask the student to pretend to be the customer and I will act as the shopkeeper, etc.). In this way, the vocabulary is concentrated in one area and we learn also something practical if a student were to find her/himself in Italy.
With more advanced students the conversations are usually more evolved and we go over complex topics like history, philosophy or science and almost always, at this level, I leave it to the student to talk about whatever interests her/him.
One risk to avoid in teaching a language is to treat it like a static subject. No language is! So I teach students a lot of "slang", not the kind you can learn from watching Jerry Springer's kind of shows, but language that Italians use in everyday life.
EXTRAS: At times I let students borrow some of my books and comics. I also own a reasonable library of Italian movies (comedies, classic dramas) that almost any Italian would know and that to some extent are part of their cultural identity. It is very hard to go to another country and fit in as much as possible without knowing what kind of entertainments they like, they talk about, etc. A little like someone coming to the US and mumbling "Oprah who?" or asking "Who is Joe Montana?" or not knowing anything about cultural trends and fashions.
CURIOSITY. While the history of Italy is long and prestigious, the country in its current form has only been in existence since 1861, first as the Kingdom of Italy (1861-1946) and then as the Italian Republic (1946 to today).
Since the country has been unified only in 1861, it should come as no surprise that in Italy there are many dialects, more or less one for each of its 20 regions due to the country's fragmentation and colonization by foreign powers. What today we call the Italian language is more or less the language of Florence that gained prestige because of major literary works by Dante, Petrarch and Boccaccio during the 14th century.
So, keep in mind that even Italians, to some extent, are learning Italian as a somewhat foreign language!
I have a Ph.D. in Statistics with a minor in Mathematics. I have taken Linear Algebra classes at the graduate level and I have used it in the theory of linear models and in linear functional analysis. I have also experience with matrix differential calculus and its applications to complex situations in econometrics and the general theory of linear models.
While completing my undergraduate degree in Economics and Business, I took one marketing class. Later, I worked for marketing research companies, once working on assessing management performance for Kellogg's Raisin Bran in terms of brand awareness and the second time doing analyses for tourist operators in Italy to advise on how to put in place the most effective advertising both internally and abroad.
I have also had some experience with data-driven marketing and the essential marketing metrics used. While not everyone agrees, I belong to the group of people that believes marketing should be treated like any other investment within a firm and judged in terms of return on investment (ROI). As a financial analyst and a statisticians I have available quite a few mathematical and accounting tools to understand and measure success of marketing strategies.
I have had an Excel spreadsheet open on my computer(s) daily for more than 20 years.
As a stock analyst and a statistician, I have learned and used most of its features.
I have worked in an environment were both getting the right answer and getting it fast
are paramount. And over the years Excel has become my trusted friend in the office as I learned feature after feature.
Except for modifying macros and/or using VBA, pretty much all features of Excel are accessible to anyone even with modest computer literacy. And with Excel 2010 the power of Excel to handle large data sets has improved considerably.
Whether you are looking for something introductory, intermediate or advanced, I am confident I can help you.
Pre-calculus (Algebra 3) lacks the rigor of calculus, but it is a very important subject, kind of an appetizer for what mathematics can do when applied to real-life situations.
Graphing functions, solving polynomial equations, exponential and logarithmic functions, sequences and series, up to matrices and the all-important notion of limit are part of any serious baggage of knowledge for students heading to college.
The challenge, in my opinion, is to get students to appreciate what they are learning. When I teach this subject, I try to come up with as many real-life uses for it as is possible and I also try to use mathematical software (Mathematica, Matlab) to show students some of the more technical nuances of the topic.
Although I studied it many years ago now, I always enjoy revisiting it when helping students. And, truth be told, pre-calculus has helped me not only in college and graduate school, but even in doing my work.
Why am I qualified to teach probability?
I was trained as a theoretical statistician when working on my PhD degree and as a result I had to learn a lot of probability. Probability is an essential mathematical tool to have in the bag for a statistician. More important, I did not only have to learn it, but also I needed to use it and still do.
What can I teach?
I can help students master the basic notions of probability, but I can also (and I have done so) work with college students on calculus-based probability courses up to the very serious measure theory-based probability taught at very advanced levels in Math and Stat PhD programs or in Mathematical Finance M.Sc's degree programs.
I have a passion for probability, arguably my absolute favorite subject and over the years I have developed a large array of examples and counter-examples to show the strengths and limitations of the theorems and how they can be applied to solve real problems in many fields.
SAT math often makes students (and many a parent as well) very nervous. While the types of problems are not more difficult than the problems a student is required to solve during regular tests in their normal classes, there is the pressure of knowing that quite a bit of one's college opportunities ride on his or her score on this test. Plus, working under pressure is not easy for most people.
My approach is requiring the student to take a sample test, seeing the overall score and checking for potential areas that reveal particular weaknesses, and working from there. Also, time management is essential. Sometimes, it is a good idea to sacrifice one question to be able to answer 3 or 4 more. In one case, I worked with a student who felt the pressure excessively by taking one question at a time, after running up and down a flat of stair each time. I called this the "athletic approach". After this student realized that he could score 650 while being winded and sweating, he realized that he could do way better by taking the test under "standard conditions". And indeed he sat his SAT without excessive apprehension reporting a score of 765.
Statistics is becoming increasingly important. Finding ways around uncertainty and making sense of collections of datasets are skills in high demand and in fact, Statistics is now part of a larger number of curricula than ever.
I have a PhD. in Statistics and a B.Sc. (cum laude) in Economics with a specialty in Econometrics. In addition, I have used applied statistics in marketing research, economic studies and financial applications. Also, I am familiar with SAS software and a few more statistical packages. I have done a lot of work in the field of linear models, regression analysis, regression graphics, categorical models and simulation/computational statistics.
What can I teach?
- I have worked with high school students on AP Statistics with good results;
- I am involved with college students taking classes in Statistics, both theoretical and applied;
- I have also helped graduate students with advanced topics at both the Master's and the PhD. levels including advanced Mathematical Statistics. From time to time I helped them with their dissertations or projects.
My teaching philosophy.
Often, students suffer a rejection towards the subject because, unfortunately, in many classes they see just a lot of formulas thrown at them. My approach is to motivate each formula I introduce, stating its function, and analyzing some of its strengths and weaknesses. For example, why is the median a better estimator than the mean in certain situations? Because it is more robust to the presence of outliers and many practical examples can be easily concocted.
I find that motivating the subject is even more important as the students who come to me are involved in more advanced statistical techniques where it is paramount to understand the underlying assumptions that make it possible to use specific models.
Track & Field
I competed in track & field for over 10 years, earlier on as a long and triple jumper and later in the decathlon. I have also coached athletes in the shot put and discus. Until not too long ago I was a master discus thrower myself.
I have competed in all events except the marathon during my time in the sport.
Trigonometry is often perceived as if it were a useless subject that deals with triangles whose angles are not 30, 60, or 90 degrees or little more. This is unfortunate because, after a first phase where students learn the basic notions, the range of tools available to solve real-life problems is quite remarkable. Several fields in physics and engineering use it, Fourier analysis is based on the notions one learns in this class and Fourier analysis is heavy "weaponry" when one uses it to solve a large variety of problems.
I have developed my own notes for this subject and I am quite proud to say that I help students to get to appreciate the subject by using as many real life problems as possible, from measuring height of buildings in several different situations, to play with acoustic waves and even analyzing the possibility of collapsing bridges when forced resonance (a trigonometry type of phenomenon of sort) gets into the picture.