Josh O. A Level Maths tutor, A Level Further Mathematics  tutor, GCSE...

Josh O.

Currently unavailable: for regular students

Degree: Mathematics (Bachelors) - Warwick University

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About me

My attitude towards learning is that a broader and less rigid learning experience allows people to understand things fundamentally, helping them in the long run.  This approach is especially useful in STEP, where papers aren’t as predictable as they are for A-Levels.  When a student doesn’t quite understand a topic, I’m welcoming, responsive and explain the topic clearly and in various ways to overcome any misconceptions.

Earlier in the academic year, sessions are usually centred on the content of one chapter and the ideas are explored properly.  This gets students to grasp how to approach problems.  Closer to exam season, many students understandably prefer to make use of past papers.  For maths, they are an invaluable resource.  My experience with mathematics has always been with Edexcel, and I’m very familiar with their A-Level syllabus.  When necessary, I read up on other exam boards’ syllabi.

I’m typically less available further in the academic year, but I’m completely freed up after my last exam on 11/06/14.

Subjects offered

SubjectLevelMy prices
Further Mathematics A Level £20 /hr
Maths A Level £20 /hr
Maths GCSE £18 /hr
.STEP. Uni Admissions Test £25 /hr

Qualifications

QualificationLevelGrade
MathematicsA-LevelA*
Further MathematicsA-LevelA*
BiologyA-LevelB
STEP IUni Admissions Test1
STEP IIUni Admissions Test2
STEP IIIUni Admissions Test1
AEAUni Admissions TestDistinction
Disclosure and Barring Service

CRB/DBS Standard

No

CRB/DBS Enhanced

No

Currently unavailable: for regular students

Questions Josh has answered

Are we able to represent linear matrix transformations with complex numbers?

Absolutely. Consider a point (a,b). This may be represented by the complex number a+bi and also by the column vector (a;b), where the semicolon means 'new line'. To translate the point by +(c,d), in complex numbers, this is done by adding c+di to a+bi.  In 2D space, this is done by adding (c;...

Absolutely. Consider a point (a,b). This may be represented by the complex number a+bi and also by the column vector (a;b), where the semicolon means 'new line'.

To translate the point by +(c,d), in complex numbers, this is done by adding c+di to a+bi.  In 2D space, this is done by adding (c;d) to (a;b).

To scale the point by a factor of r, in complex numbers, this is done by multiplying by r.  In 2D space, we do the very same thing.

To rotate the point about (0,0) by angle t in the counterclockwise direction, in complex numbers, we do this by multiplying by e^it. In 2D space, we multiply on the left hand side by the matrix ((cost,-sint);(sint,cost)).

To conclude, if we were to translate a point (a,b) by +(c,d), scale it by factor r and rotate it about the origin by angle t in the counterclockwise direction, then the following are two representations of it:

(a+bi)(re^it)+(c+di)

r((cost,-sint);(sint,cost))(a;b)+(c;d)

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1 year ago

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