First, let y=k/x. Now, we know that y=12 when x=3, so we can solve for k: 12=k/3, or k=12*3=36. Now we have y=36/x. So y=36/20 when x=20. Thus, y= 9/5. Hope this helps!

- (877) 999-2681
- Become a Tutor
- Become a Student
- Sign In

$75/hr

Background check passed
as of 3/18/14

Usually responds in about 1 hour

Send Christopher a message explaining your needs and you will receive a response by email.
**
Have you already emailed Christopher or another tutor? If so, you have an account!
Sign in now
**

If you select this option, WyzAnt will ask interested tutors to contact you by email if they are able to help. A maximum of five different tutors will email you and none of your personal information, including your email address, will be released.

“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” - Albert Einstein

Looking for a math oracle? Look no further! I specialize in tutoring math subjects for students in high school and college. I have tutored math since taking calculus when I began holding after-school sessions with groups of my peers. I have experience tutoring a wide array of subjects in math: from prealgebra to precalculus, to multivariable calculus and linear algebra. I help you achieve your goals and help you understand mathematical reasoning with utmost clarity. My tutoring philosophy combines patient, enthusiasm and positive reinforcement. Your goals become my goals!

A little bit about myself: I am a recent graduate of the M.S. degree program in Mathematics at Tufts University where I focused on the three major cornerstones of Contemporary Mathematics: Analysis (Real & Complex), Abstract Algebra, and Geometry/Topology. I completed my undergraduate education at Saint Anselm College where I majored in Mathematics, with a secondary major in Classics. I graduated in the top 5% of my class from St. A’s with an Honors B.A., Magna Cum Laude. I will be attending the University of Amsterdam in the Fall of 2016 for a M.Sc. degree in Mathematical Logic, Language, and Computation (metamathematics). There, I will be investigating how mathematical theory flourishes, i.e., what fundamental logical structures influence the rich development of certain operations over others. Thank you for considering me!

My availability is flexible during the week, both afternoons and evenings, and the weekend. Have any scheduling questions? Shoot me a line!

Christopher has tutored my daughter in Algebra II for a month and a half. He has been an incredible resource and responds to emails right away. He is extremely adept at breaking down complex problems into a systematic process that my daughter can understand. Her confidence in her math skills have steadily increased due to his teaching style. Christopher truly is interested in helping his students succeed and connecting with them; I highly, highly recommend him!

Chris tutored me in Calculus II and I would highly recommend his tutoring for anyone. He was easy to work with and genuinely wanted to help me understand the subject, as well as succeed in the course. His schedule was flexible so it was very easy to schedule meetings. It was also easy to get in touch with him if I had any questions. He always encouraged me to call or text him at any time if I had any concerns. In addition, Chris has a very in-depth knowledge of Calculus so he was able to help me work through any problem by explaining it to me in a way that I could understand.

Chris is an incredible tutor with extensive knowledge in math. I was enrolled in a statistics class at Boston University and was very concerned that I would not be able to find a good enough tutor to help me, but Chris could answer every question I had and more. He was very patient and willing to explain concepts in numerous ways until I fully understood what I had troubles with. I was able to email or text him at anytime of the day and could expect a prompt reply; it was very easy to find a time and place that fit both of our schedules. I highly recommend him to anyone who has trouble with or is just a little unsure of the things that they are studying.

Christopher is a talented equation of interpersonal skills, logic, reasoning, and above all, I recommend his services to any student for his unparalleled patience and understanding. The complicated and intricate math processes that can often leave one feeling lost and frustrated, such as I was, all seemed to fade with Chris's help. Although he makes it look effortless, he truly wants his students to excel and understand the mathematical problems at hand. With a master skill set and detail-oriented teaching style, he will take the time with you to review any topic that needs immediate attention. You, the student, are a product of Chris's work, and he prides himself on his superior abilities to process, analyze, and assess almost any mathematical problem. I am glad I chose Chris as my tutor. The result? I increased my calculus skills, and do not feel as overwhelmed when tackling the subject alone.

Chris Is among one of the best tutors I have ever worked with. He is patient, listens, and explains everything in great detail. Chris has skills that are above anything I have ever seen. He knows his material and is an expert in all aspects of Algebra.

Chris is an excellent tutor. Chris is bright, strategic, analytic, resourceful and respects where you are with your work. A good tutor like Chris positions himself in the eyes of those he helps. He helped me re-analyze my logic progress and helped me build a realistic plan of action under time constraints. Logic is my most challenging topic. Chris' tutoring method helped make my work accessible, approachable, achievable and actionable. Chris is excellent for the price-point.

Chris is an extremely intelligent bright talented person. Not too many have I met like him. He brings a vast amount of knowledge and skill to the table and is very patient. Highly recommendable!

Math:

ACT Math, Algebra 1,
Algebra 2,
Science:

Philosophy
Business:

GMAT, GRE
Test Preparation:

ACT Math, GMAT, GRE, PSAT, SAT Math
Corporate Training:

GMAT, Statistics
Approved subjects are in **bold**.

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.

Are you struggling to relate Algebra and Geometry to Algebra II? I'm here to be your Oracle!

I've tutored this subject for many years and I enjoy doing so! I've studied ABSTRACT Algebra in College and Graduate school, where I learned WHY algebra works, not just HOW it works; there is a rich history in the development of this wonderful subject.

Topics include, but are not limited to:

Polynomials, Factoring, Roots, Exponentials/Logarithms, Complex Numbers, Parabolas, Circles, Ellipses, Hyperbolas, Angle measures, Trigonometry, Trigonometric Identities, Sequences, Rational Exponents, Radical Functions and Expressions, Functions, Systems of Functions/Inequalities, Quadratic Functions, Matrices.

In College, I studied Calculus both intensively and extensively. Intensively by studying Calculus I, II, III and Differential Equations; but, more importantly, by understanding the theoretical and proof-based foundation of the subject through Advanced Calculus I-II courses. I studied the subject extensively by seeing its application in courses such as Numerical Analysis, Complex Variables, Calculus-based Physics and Calculus-based Statistics.

In Graduate School, I explored the theoretical aspect of Calculus more thoroughly by taking Mathematical Analysis I-II, Measure/Integration Theory, and Complex Analysis. The rigorous treatment and proof-approach of n-dimensional Calculus, through the tools of logic, has taught me why Calculus works, not just how it works.

If you are taking any subjects of Calculus that I've mentioned above, please contact me and I'll be more than happy to provide you with some very helpful insight into this fundamental and timeless subject.

I've taken Differential Equations in college and graduate school: Ordinary Differential Equations as an undergraduate, Partial Differential Equations as a graduate student.

I can help you in the following areas:

1). Classification of Differential Equations; Initial-Value Problems, Boundary-value Problems, and Existence of Solutions.

2). Exact Differential Equations and Integrating Factors; Separable Equations; Linear and Bernoulli Equations; Orthogonal and Oblique Trajectories.

3). The Homogeneous Linear Equation with Constant Coefficients; The Method of Undetermined Coefficients; Variation of Parameters; The Cauchy-Euler Equation.

4). Power Series Solutions About an Ordinary or Singular Point; Bessel's Equation and Bessel Functions.

5). The Laplace Transform.

If any of these topics leave you scratching your head, please reach out; I'd be glad to provide clarity!

I've studied Discrete Mathematics in College when I took Discrete Math I-II in preparation for graduate school. I'm finding a lot of computer science majors are required to take this course. Usually mathematical induction is the topic which leaves the student baffled and eager to seek a supplemental voice; I'm here to be that voice!

Discrete Math I-II topics that I can help you with are the following:

Basic Logic, Set Theory, Relations, Quantifiers, Algorithms, Counting Methods, De Morgan’s Law, Logical Connectives, Truth Tables, and Relationships Between Statements, Recurrence Relations, Graph Theory, Trees, Boolean Algebra, Automata, and Grammars.

I've studied finite mathematics at the undergraduate level as well as the graduate level. In College, I took Discrete Math I-II, Linear Algebra, Finite Geometry, and Number Theory.

Also, as a M.S. student, I took Abstract Algebra I-II which included a rigor treatment of finite groups, rings and fields. I've tutored my peers in these subjects as well.

The title of this subject can be misleading: it sounds easy but it's actually more abstract than it sounds. It can be difficult to conceptualize some topics in this subject, but don't worry I am here to help! Engineering majors who are required to take this class will find it to be one of their more difficult math classes.

In College, I was instructed in this subject using Gilbert Strang's book Linear Algebra, 3rd edition, Wellesley-Cambridge Press. I highly recommend this book.

If you are struggling with any of the following areas, please reach out -I will deliver clarity and comfort:

1). Vectors

2). Solving Linear Equations

3). Vector Spaces and Subspaces

4). Orthogonality

5). Determinants

6). Eigenvalues and Eigenvectors

I've studied Basic Logic and Mathematical Logic. I will be attending the University of Amsterdam in the Fall of 2015 for a M.Sc. degree in Mathematical Logic and Computation, so please feel free to reach out if you have any questions or struggles.

For Basic Logic, I can provide insight into: Set Theory, Relations, Quantifiers, Algorithms, Counting Methods, De Morgan’s Law, Logical Connectives, Truth Tables, and Relationships Between Statements.

For Mathematical Logic, I can provide insight into: Terms and Formulas in First-Order Languages, Induction in their Calculus, Structures and Interpretations, Satisfaction and Consequence Relations, Formalizations, and Sequent Calculus.

I've taken a variety of Philosophy classes which I thoroughly enjoyed: Philosophy of Nature/Man, Ethics, Philosophy of Mind, Roman Philosophy, Greek Philosophy, and Epistemology. I did my Honors College Thesis on the Epistemology of the Geometry of Space. If you are looking for someone to give you an objective, or subjective, point of view for one of your class, please send me a message. I read a lot of philosophical books in my leisure time. Let's have a dialogue!

Do you have a son or daughter who struggles with fractions? Operations with fractions? Or trouble finding the volume of a solid?

No need to fret, I can help break down the problems into smaller parts that are much more understandable and fun to learn. Whether it's finding surface areas, percentages, polynomials, inequalities, or number sequences, I can supplement the problems one's struggling with so there's complete clarity and enjoyment in learning this subject.

Tutors have the ability to create educational resources and share them with the WyzAnt community. Here are some of the resources created by Christopher. View all of Christopher’s resources

First, let y=k/x. Now, we know that y=12 when x=3, so we can solve for k: 12=k/3, or k=12*3=36. Now we have y=36/x. So y=36/20 when x=20. Thus, y= 9/5. Hope this helps!

x=1/x+1 becomes x-1=1/x which is then x(x-1)=1 factoring we get x^2-x=1 completing the square we get (x-.5)^2 -.25=1 therefore, (x-.5)^2=1.25 and now we take the positive sq root of both sides to get (x-.5)= sqrt(1.25) thus...

This function is surjective but not injective: You can attain any z value in the codomain simply by letting x=0 and y=3z for z positive, by letting x,y=1 for when z=0, and by letting x=2 and y=-z for z negative; therefore surjective. Now let (x1,y1)=(2,3) and...

**Efficient, organized, and accommodating! ** —
Christopher has tutored my daughter in Algebra II for a month and a half. He has been an incredible resource and responds to emails right away. He is extremely adept at breaking down complex problems into a systematic process that my daughter can understand. Her confidence in her math skills have steadily increased due to his teaching style. Christopher truly is interested in helping his students
...

Standard Hourly Fee: $75.00

Cancellation: 8 hours notice required

*Please note:
Cancellation Fee is one hour of the student's rate.*

Christopher will travel within 40 miles of Somerville, MA 02144.

Your first hour with any tutor is protected by our **Good Fit Guarantee:** You don’t pay for tutoring unless you find a good fit!

- Somerville, MA Art Tutors -
- Somerville, MA Business Tutors -
- Somerville, MA Computer Tutors -
- Somerville, MA Corporate Training Tutors -
- Somerville, MA Elementary Education Tutors -
- Somerville, MA English Tutors -
- Somerville, MA History Tutors -
- Somerville, MA Homeschool Tutors -
- Somerville, MA Language Tutors -
- Somerville, MA Math Tutors -
- Somerville, MA Music Tutors -
- Somerville, MA Science Tutors -
- Somerville, MA Special Needs Tutors -
- Somerville, MA Sports/Recreation Tutors -
- Somerville, MA Test Preparation Tutors

Christopher F. passed a background check on 3/18/14. The check was ordered by Christopher through First Advantage. For more information, please review the background check information page.

After sending a message to Christopher, you will be able to order a new background check for $7.99. As part of your tutor selection process, we encourage you to run updated background checks. Please also review the safety tips for hiring tutors.