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# Algebra2:- Mathematical induction, binomial theory and its applications, exponential and logarithmic series

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples

Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.

Mathematical induction includes :- principles of Mathematical induction and some useful results, binomial theory and its application includes :- binomial theorem, greatest term, multinomial theorem, properties of binomial coefficient, binomial theory for any index. The exponential and logarithmic series includes :- The number e, some important results, logarithmic series.

I will teach each and every section with lots of examples and illustrations.

Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.

Mathematical induction includes :- principles of Mathematical induction and some useful results, binomial theory and its application includes :- binomial theorem, greatest term, multinomial theorem, properties of binomial coefficient, binomial theory for any index. The exponential and logarithmic series includes :- The number e, some important results, logarithmic series.

I will teach each and every section with lots of examples and illustrations.

## Location

Online via webcam

## About Me

I am a resident of Kerala, India. I have been a part-time tutor for the last 5 years. I had taught Mathematics at various private institutes in order to help the students to perform well in highly competitive examinations. I have taken classes for IIT aspirants in Kerala for both JEE main and Jee advance examinations. Apart from that, I had taught students from both higher secondary and secondary level. Earlier, I had cleared all India IIT JEE mains and IIT JEE advance examination with 90/120 and 132/168 respectively in Mathematics (2015).Recently, I received offer letters from University of Manchester, University of Birmingham, Heriot- watt university, and University of liverpool for pursuing MSc applied Mathematics with a partial funded scholarship. I have also been offered an admission to famous Joint MSc InterMaths Math-Mod programme for pursuing Masters in Mathematical modelling with a fully funded scholarship. This Program is jointly offered by three European reputed Universities and the programme is supported by European Union.

I have been granted an adfmission to the famous Inter Maths 2 year Erasmus Mundus joint master degree interdisciplinary Mathematics programme with a fully funded scholarship. This program is jointly offered by 5 reputed European reputed Universities and the programme is supported by European Union.

I have been granted admission to Inter Maths double degree MSc program in Applied Mathematics along with fully funded scholarship. This program is jointly offered by two European reputed universities.

Earlier, I was admitted to University of Texas Rio Grande Valley, USA for MS Mathematics and was awarded a graduate teaching assistantship along with deans graduate assistantship for the Fall semester 2020. But I dropped the offer due to the

outbreak of Covid-19.

I was previously selected for 3-months summer internship program at IST Austria in 2020 under the supervision Mr Marco Mondelli. However, the program was cancelled due to the outbreak of Covid-19. My aim was to work on a short project titled "Polar codes under a fuzzy environment". The admission to

this program was mainly based on the previous literature review written by me regarding the Polar codes.

I have also presented a research paper in the Fuzzy Mathematical Analysis and Advances in computational Mathematics (FMAACM 2021) international seminar. The seminar was conducted by Pondicherry University in ally with DST india, UGC-SAP india, MOST Israel, Indo-Israel joint project, Soft Computing journal (springer), and book series "studies in fuzziness and soft computing" (springer nature). My paper is going to be published in this reputed book series. Apart from that, I had completed seven research papers/articles and I have already

submitted six research articles/papers to various reputed international

journals and seminars/conferences.

I have started the work on another research paper titled "A new

arithmetic operators on Fuzzy Matrices". This research paper is about to

be completed with in three months.

## Education

I completed 5 year Integrated BSc-MSc from Pondicherry university, India. Recently, I got offer letters from various universities in UK. I planning to join Heriot-Watt university for MSc Applied Mathematics.## Experience / Qualifications

I have been a part time mathematics tutor for the last 5 years. I have taught students both in online and offline modes.I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Algebraic inequations chapter includes :-solving rational algebraic inequations, to find solutions of linear inequations in two variables. Logarithm includes:- laws of logarithms, some useful results in logarithms, and of system of logarithms. Inequalities includes:- elementary properties of inequalities, some types of new inequalities, applications of inequalities to find the greatest and least values. Set theory includes:- types of sets, operation on sets, laws of algebra of sets, results in set theory. Cartesian products of sets and relation chapter includes:- definition of relation including examples, types of relations, composition of relations. Functions includes:- function as a relation, function as a correspondence, number of functions, kinds of functions, composition of functions, inverse of function. Finally, complex numbers includes:- integral powers of IOTA(I), imaginary quantities, complex numbers, fundamental operations on complex numbers, modulus of a complex number, representation of complex numbers( geometrical form, vectorial form, trigonometrical form or polar form, eulerian form), some important results on modulus and argument, geometry of complex numbers, complex number as a rotating arrow in the argument plane, some important results, equation of straight line, de moivere's theorem, logarithm of a complex number.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Sequence and series includes:- arithmetic profession, geometric progession, harmonic progession, arithmetico- geometric sequence, sum to n terms of some special series , summation of some special series. Quadratic expressions and equations includes :- real polynomial, complex polynomial, degrees of a polynomial, polynomial equation, roots of an equation, position of roots of a polynomial equation, descarte's rule of signs, relation between roots and coefficients, formation of a polynomial equation, transformation of equation, roots of a quadratic equation with real coefficients, quadratic expression and its graph, position of roots of a quadratic equation, common roots, maximum and minimum value of a rational expression, condition for resolution of a quadratic function into linear factors, algebraic interpretation of rolle's theorem. Matrix includes:- types of matrices, algebra of matrices, properties of matrices, transpose of a matrix, determinant of a square matrix, adjoint of a matrix, inverse of a matrix, orthogonal matrix, rank of a matrix, system of simultaneous linear equations. Determinant includes:- determinant, minors and cofactors, properties of determinant, product of determinant, differentiation of determinant, application of determinant, system of linear equations.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Cartesian coordinate system includes:-
Cartesian coordinate system:- distance between two points, area of triangle, section formulae, terms related to triangle, translation of axes, rotation of axes. Straight lines :- slope of a line, angle between two lines, different forms of equation of a line, point-slope form, distance form, position of points relative to a line, intersection of lines, lines parallel and perpendicular to a given line, distance of a point from a line, area of a parallelogram, Inge of a point with respect to line, equations of a straight lines passing through a point and making a angle with a given line, lines through the intersection of two lines, equations of the bisectors, acute and obtuse angle bisectors, locus and its equation. pair of straight lines:-joint equation of a pair of straight lines, angle between the pair of lines, general equation of second degree, lines joining the origin to the points of intersection of a line and a curve. Circle:- standard equation of a circle, particular cases of central form, general equation of a circle,circle passing through three points, diameter of a circle, interception of the axes, position of point with respect to a circle, equation of a circle in a parametric form, intersection of a line and circle, tangent to a circle, normal to a circle, pair of tangents, length of tangents, director circle, chord of contact, chord bisected at a given point, pole and polar, common tangents of two circles, common chord, angle of intersection of two circles, radical axis, family of circles, co axial system of circles. Parbola:- conic sections, analytical definition, general equation of a conic, parabola in its standard form, other standard forms of parabola, terms related to parabola, parametric equations of a parabola, point and parabola, parametric equations of a chord, a line and a parabola, equation of tangent, results on tangents, common tangents, angle intersection of two curves, normals, results on normals, number of normals and conormal points, pair of tangents, chord of contact, chord. Bisected at a given point, diameter, pole and polar, length of tangent, sub-tangent, normal and sub normal. Ellipse:- definition, standard form of ellipse, terms related to ellipse, other forms of ellipse, equation of ellipse referred to two perpendicular line as axes, parametric co ordinates and equations, equation of chord, a line and an ellipse, tangent, pair of tangents and their chord of contact, director of circle, normal, number of normals and conormal points, chord bisected at a given points, pole and polar, diameter and its equation, conjugate diameter and its properties. Hyperbola:- standard equation of the hyperbola, conjugate of hyperbola, parametric co ordinates, position of a point with respect to a hyperbola, intersection of a line and a hyperbola, tangent to a hyperbola, number of tangents, normals to a hyperbola, number of normals drawn from a point, pair of tangents and their chord of contact, chord bisected at a given point, pole and polar, diameter and its equation, asymptotes, rectangular hyperbolaand its properties, tangent to a rectangular hyperbola), results on rectangular hyperbola.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Calculus 2 includes :-
Mean value theorems:- rolle's theorem, Lagrange s mean value theorem. Increasing and decreasing functions:- definitions, monotonic function band it's properties. Maxima and minima:- definition, local minima and maxima and properties. Indefinite integrals:- formulas of integration, types of integration, some important integrals. Definite integrals:- definition, geometrical interpretation of definite integral, evaluation of definite integrals by substitution, properties of definite integrals, integral function, gamma function, summation series using definite integral as the limit of a sum. Areas of bounded region:- definition, algorithm, problems.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Calculus 1 includes:-
Real functions:- domain &range of real function, types of real functions& operations, periodic functions, even&odd function, extension of functions. Limits:- Left and right hand limits, intermediate forms and their evaluation, algebraic limits, types of limits, evaluation of limits by various methods (eg- De' L' Hospitals rule). Continuity and differentiability:- continuity at a point, definition of continuity, discontinuous function, properties of continuous function, differentiability at a point, differentiability in a set. Differentiation:- rules for differentiation and types of differentiation, differentiation of determinants, higher order differentiations. Tangents and normals:- slopes of a tangent and normal, equation of tangent and normal, angles of intersection of two curves, length of tangent, normal, sub tangent and subnormal. Derivatives as a rate measure:- differentials, errors, approximations. Differential equations:- definition, degree of a differential equation, types of differential equations, formation of a differential equations, differential equations of first order and first degree, methods of solving a first order first degree differential equations, equations in a variable seperable form and types, orthogonal trajectories of a curve

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Trigonometry 2 include:-
Trigonometric equations band inequations:- solutions of Trigonometric equations, various solved problems.
Heights and distances :- angles of elevation and depression, m-n theorem, some useful results, various solved problems,
Solution of triangles:- solution of a right angled triangle, solution of a triangle in general, some useful results

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Trigonometry 1 includes:-
Trigonometric ratios and identities:- basic formulas, domain and range of trigonometrical functions, sum and difference formula, sum and difference into products, products into sum or difference, Trigonometric ratios of the sum of three or more angles, Trigonometrical ratios of some important angles, maximum and minimum values.
Properties of circles and triangles connected with trigonometry:- properties of triangle and its theorems, circles connected to a triangle and theorems, Ptolemy's theorem, area of a cyclic quadrilateral, circum-radius of a cyclic quadrilateral. Inverse trigonometry:- inverse of a trigonometric function, properties of inverse trigonometric functions, solved problems.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics and statistics is very easy to learn. I will teach you with good examples.
Nowadays, mathematics and statistics are used as interdisciplinary in various other fields like ecology, biology, and so on.
Statistics includes:-
Measures of central tendency:- arithmetic mean and types, properties of arithmetic mean, weighted arithmetic mean, geometric mean, geometric mean of combined series, harmonic mean, median , its types and its algorithm, quartiles , its types, mode and its types, symmetric distribution. Measures of dispersion:- range, quartile deviation, mean deviation and its algorithm, variance, standard deviation and its algorithm, variance and its types.

I can provide you classes from the basic levels to advance levels of all these topics listed above (see heading). Students need not be panic. Mathematics is very easy to learn. I will teach you with good examples
Nowadays, mathematics is used as interdisciplinary in various other fields like physics, biology, and so on.
Vectors and 3-d geometry includes :-
Algebra of vectors:- representation of vectors, types of vectors, algebra vectors, position vector, section formula, collinear and non collinear vectors, collinear points, components of vector, coplanarity, linear independence and dependence, vector along bisector. Scalar and vector products of two vectors :- the scalar or dot product and its properties, angle between two vectors, applications, tetrahedron, vector or cross product and its properties, applications, area of quadrilateral, moment of a force, moment of a couple. Scalar and vector products of three vectors:- scalar triple product and its properties, applications, volume of tetrahedron, vector triple product and its properties, applications, reciprocal system of vectors, solutions of vector equations. 3d coordinate system:- co ordinates of a point in space, signs of co ordinates of a point, distance formula, section formulae, direction cosines and direction ratios, angle between two lines. Plain and straight line in space:- plane, intercept form of a plane, vector equation of a plane, equation of a plane in a Normal form, equation of a plane in a parametric form, plane parallel to a given plane, straight line, reduction from unsymmetrical form to a symmetrical form, angle between two lines, plane through intersection of two planes, distance of a point from a plane, planes bisecting the angles between two given planes, distance of a point from a line, image of a point in a plane, reflection or image of a point in a straight line, shortest distance between two straight lines and two skew lines, angle between a plain and a line , condition of a line to lie in a plane, coplanarity if two lines.

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from $27.82Online via webcam

### 100% Satisfaction Guarantee

### Good-fit Instructor Guarantee

If you are not satisfied after your first lesson, Apprentus will find you another instructor or will refund your first lesson.

### Online reputation

- Instructor since July 2021
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from $27.82Online via webcam

### Good-fit Instructor Guarantee

If you are not satisfied after your first lesson, Apprentus will find you another instructor or will refund your first lesson.

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