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rktpro

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Posts posted by rktpro

  1. Is it right, that all humans have to 99% the same DNA?

    Does an african have to 99% the same DNA as an asian?

     

    From where you got the 99% fact?

    It is though right that humans have same genetic composition and hence fairly similar and not identical DNA structure.

  2. I came across a formula derived by Ankur Tiwari, which he says enables division by zero.

     

    The website claims

     

    This formula enables us to divide in a unique way without using denominator. This formula is based on the principle that, If the value of X divided by Y (X/Y) is A than by using this formula we can find out A without dividing X by Y directly, that means without dividing X by Y we can find out its value. This is the reason why ‘Bhartiya New Rule for Fraction’ is capable of diving by Zero.

     

    The interesting points in regard of this formula are :-

     

    1.‘Bhartiya New Rule for Fraction’ is based on present phenomenon and rules of mathematics.

     

    2. It is very simple and easy formula.

     

    3.Greatest benefit of ‘Bhartiya New Rule for Fraction’ is that it is capable of dividing by Zero and giving its value as an integer.

     

    4.‘Bhartiya New Rule for Fraction’ can be used to find out the value of four not defined trigonometric ratios tan90, cosec0, sec90, cot0. So that these values can be utilized in the field of astronomy and other fields related to mathematics.

     

    5.If in place of simple division (X/Y), ‘Bhartiya New Rule for Fraction’ is used in any digital electronic device as its processing command for division in processor, it will results in permanently elimination of ‘divide by Zero’ error from that device.

     

    How would it affect mathematics? Is there a fallacy in there?

    Let us discuss...

     

     

     

     

  3. Limestone is a form of calcuim carbonate which is slightley soluble in water producing dissolved calcuim and bicarbonate ions, would you expect the water to be hard or soft?

     

    What would you expect to occur to the concentration of calcuim, magnesium and sodiaum ions in hard water when water is artificailly softened by passing through an ion- exchange filter?

     

     

    The second question itself is a hint to the first one.

  4. But we should not be able to see who made those votes, it would only cause trouble and unfair revenges.

     

    Yes, everyone would be derailing the discussion and abusing those who gave negative.

    But, it can be highly insightful for some to know who agree with them and who not.

  5. As a reference book I keep a copy of the Handbook of Mathematics by Bronshtein-Semendyayev. It has no instructional material or exercises but it covers everything you've listed above.

     

    I am not looking for reference books currently but full text books type. But, Thanks!

  6. I am looking for books which are not just typical math. books by just giving least theory and difficult exercise. I am looking for a book that develops the real thinking ability and along with it covers problem soling skills by providing interesting questions. If you know about a book covering only one or two chapters of the following list, I will still love to read that.

    Syllabus

     

     

    PERMUTATIONS AND COMBINATIONS

    Fundamental principle of counting. Permutations and Combinations, derivation of

    formulae and their connections and simple applications.

     

    MATHEMATICAL INDUCTION

    Principle of Mathematical Induction and its simple applications.

    BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS

    Binomial theorem for positive integral indices, general term and middle term,

    properties of Binomial coefficients and simple applications.

     

    SEQUENCES AND SERIES

     

    Arithmetic and Geometric progressions, insertion of arithmetic, geometric means

    between two given numbers. Relation between A.M. and G.M. Sum upto n terms of

    special series n, n2, n3. Arithmetico - Geometric sequence.

     

    TRIGONOMETRY

    Trigonometric functions. Trigonometrical identities and equations. Inverse

    Trigonometric functions, their properties and applications.

    COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    Complex numbers as ordered pairs of reals. Representation of complex numbers in

    a plane. Argand plane and polar representation of complex numbers. Algebra of

    complex numbers, modulus and argument (or amplitude) of a complex number,

    square root of a complex number, triangle inequality. Quadratic equations in real

    and complex number system and their solutions. Relation between roots and coefficients,

    nature of roots, formation of quadratic equations with given roots.

     

     

    SETS, RELATIONS AND FUNCTIONS

    Sets and their representations. Union, intersection and complement of sets and their

    algebraic properties. Power Set. Relation, types of relations and equivalence

    relation. One-one, into and onto functions and composition of functions. Real -

    valued functions, algebra of functions, polynomials, rational, trigonometric,

    logarithmic and exponential functions, inverse functions. Graphs of simple

    functions. Even and odd functions.

     

    LIMIT, CONTINUITY AND DIFFERENTIABILITY

    Limit and continuity of a function, limit and continuity of the sum, difference, product

    and quotient of two functions, L'Hospital rule of evaluation of limits of functions.

    Differentiability of functions. Differentiation of the sum, difference, product and

    quotient of two functions. Differentiation of trigonometric, inverse trigonometric,

    logarithmic, exponential, composite and implicit functions; derivatives of order up

    to two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives:

    rate of change of quantities, monotonic - increasing and decreasing functions,

    maxima and minima of functions of one variable, tangents and normals.

     

     

    INTEGRAL CALCULUS

    Integral as an anti-derivative. Fundamental integrals involving algebraic,

    trigonometric, exponential and logarithmic functions. Integration by substitution,

    by parts and by partial fractions. Integration using trigonometric identities. Definite

    Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite

    integrals. Evaluation of definite integrals. Applications of the integrals:

    determining areas of the regions bounded by simple curves in standard form.

     

    DIFFERENTIAL EQUATIONS

    Ordinary differential equations, their order and degree. Formation of differential

    equation whose general solution is given. Solution of differential equations by the

    method of separation of variables. Solution of homogeneous differential equations

    and linear first order differential equations.

     

    CO-ORDINATE GEOMETRY

    Cartesian coordinate system, distance formula, section formula, locus and its

    equation, translation of axes, slope of a line, parallel and perpendicular lines,

    intercepts of a line on the coordinate axes.

    Straight lines : Various forms of equations of a line, intersection of lines, angles

    between two lines, conditions for concurrence of three lines, distance of a point

    from a line, equations of internal and external bisectors of angles between two lines,

    coordinates of centroid, orthocentre and circumcentre of a triangle, equation of

    family of lines passing through the point of intersection of two lines.

    Circles, Conic sections : Standard equation of a circle, general form of the equation

    of a circle, its radius and centre, equation of a circle when the end points of a

    diameter are given, points of intersection of a line and a circle with the centre at the

    origin and condition for a line to be tangent to a circle, equation of the tangent.

    Sections of a cone, standard equations and properties of conic sections (parabola,

    ellipse and hyperbola), condition for y = mx + c to be a tangent and point (s) of

    tangency.

     

    THREE DIMENSIONAL GEOMETRY

    Coordinates of a point in space, distance between two points, section formula.

    Direction ratios and direction cosines of a line joining two points, angle between

     

    two intersecting lines. Coplanar and Skew lines, the shortest distance between two

    lines. Equations of a line and a plane in different forms, intersection of a line and a

    plane.

     

    VECTOR ALGEBRA

    Scalars and vectors, addition of vectors, components of a vector in two dimensional

    and three dimensional spaces, scalar and vector products scalar and vector triple

    product.

     

    MATRICES AND DETERMINANTS

    Matrices, algebra of matrices, types of matrices, elementary row and column

    operations. Determinant of matrices of order two and three. Properties of

    determinants, area of triangles using determinants. Adjoint and inverse of a square

    matrix. Test of consistency and solution of system of linear equations in two or

    three variables using inverse of a matrix.

     

    STATISTICS AND PROBABILITY

    Measures of Dispersion: Calculation of mean, median, mode of grouped and

    ungrouped data. Calculation of standard deviation, variance and mean deviation

    for grouped and ungrouped data.

    Probability: Probability of an event, addition and multiplication theorems of

    probability, Baye’s theorem, probability distribution of a random variable,

    Bernoulli trials and Binomial distribution.

     

    Any help is highly appreciated!

  7. I have not read the text but isn't it that it has nothing to do with the motion of planets and more to do with the Sun God and his chariots i.e the way he moves from Uttarayana and Dakshinayana.

     

    It is interesting to note that both the Mayan and the Hindu calendar start with the same starting dates around 3102BCE but the Hindu calendar doesn't end on this year, it continues for 432000.

     

    Yes, it is based on Uttarayana and Dakshinayana.

  8. Vastor, for standard deviation, as I understand, you have to take any larger mean and subtract all other from it.

     

    EDIT: For example, say you take a larger mean x, then the standard deviation for the first frequency would be x-(mean of the frequency)

  9. Because the words Krish and Kris if spoken the quality of the sound vibration you hear is more or less the same. Or they are one. Whereas the last two letters NA & TO sounds different. This philosophy of ONENESS & DIFFERENCE in sanskrit ACINTYA BEDA ABEDA TATTVA authored by Sri Caitanya Mahaprabhu ( 1486-1534 ) reconciles the two philosophies ADVAITA ( monism ) & DVAITA ( dualism ).

     

    Sri Caitanya Mahaprabhu's original teachings have always proved devotion to be the ultimate path. And even those who debated about the shastras were not liked by him.

  10. The Hindu for God is Krishna. The last two letters of Krishna and Kristo ( Greek God ) are NA and TO. Incidentally if you fuse NA and TO, you come up with word NATO. Does it ring a bell? NATO is the acronym for North Atlantic Treaty Organization. If you re-arrange again these four letters you come up with the word ATON.

     

    Why don't you take the first letters from the two words? Why last?

  11. And rajakrsna,

    You combine the Gods of Bible and Hindu Scriptures. Is there any evidence in either of them which states that the God of the other text exist. Say, in Bible. is it there about Vishnu?

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