College Grade Math

• Math

  What is math? Math is a language from which most of the students gets fear. It can define, as the study of measurement, properties and relationship of quantities using Numbers and symbols. More precise, we can say that it is the study of numbers ... Read More

  • Number Sense

    As a child many have difficulty to understand maths. It may be due to the lack of common sense. There is a way through which the children can love maths by providing it the knowledge of numbers using real world examples. This is all about th... Read More

    • Significant Figures
      Significant figures can be defined as digits which are used to express a number with desired level of accuracy. It generally describes the uncertainty in the value and hence used to find accuracy of number. The significant number ... Read More
  • Analytical Geometry

    Analytical Geometry is the part of the Algebra. It is basically concerned with the points, lines, circles, and other shapes that are the part of the geometry. In analytical geometry points are defined as the coordinate of (x,y) and... Read More

    • Polar Coordinates
      Polar coordinate is a method of presentation of points in the plane with use of Ordered Pair. This polar coordinate system comprises of an origin, pole, a Ray of specific angle and a polar axis. The polar axis is any line which initiat... Read More
    • Hyperbola
      Hyperbola definition states that a line which has curve shape is known as hyperbola or we can say that both focus (a fix Point) and directrix are always in the same ratio. It is just like a conic section. Conic section looks like a cone shape ... Read More
    • Line in a Coordinate Geometry
      In the coordinate Geometry two lines are present one is known as vertical line and other is defined as horizontal line. Now, we will see what is vertical and horizontal line in a coordinate geometry? If the x- coordinate of... Read More
    • Conic Sections and Equations of the Second Degree
      Conic section can be defined as a curve that is obtained by Intersection (Cartesian product) of a cone with a plane. In analytic Geometry conic section can be defined as an algebraic curve that has ... Read More
  • Discrete Math

    Discrete Math has a wide application in the modern mathematics. Discrete mathematics is generally used in decision mathematics. In this mathematics, we study about objects, set and graphs. Before studying discrete mathematics you must ha... Read More

    • Logic of Compound Statements
      A statement consists of one or more sub statements named as compound statement and these sub statements are connected by one or more logical connectives. As the name suggests a compound statement refers the statement form.
      ... Read More
    • Matchings in Graphs
      Matching in graphs is complete Set of edges which is without the common vertices. Matching graph theory can be an entire graph without the common vertices wholly consisting of edges. The maximum matching is a matching which has the l... Read More
    • Finding the Optimum
      The selecting of best element among the available alternatives is refereed as the mathematical optimization. If we consider the most simplest case of finding the optimum problem arouse out of function which contains its minimization ... Read More
      • Traveling Salesman
        Traveling Salesman Problems is a method that can be used to find the minimum distance that a traveling salesman has to travel such that he travels all the places at most once. There can be any number of places that we can consider in ... Read More
    • Trees in Discrete Mathematics
      A tree is a graph which contains not only a data structure of Set of elements but also the connection among all the elements. The concept of trees was given by Mathematician ‘Cayley’ in the year 1857.
      
      A tree in discrete ... Read More
    • Graphs in Discrete Mathematics
      Discrete mathematics is a distinct mathematical term rather than being continuous term. Graph, integers, etc. are the part of discrete mathematics it excludes the topics such as of Calculus and analysis, etc. or in short w... Read More
    • Graph Coloring
      The graph coloring represents the painting of the graph or we can say that the labeling of the graph with different types of colors. This technique is very much helpful from the Point of view of differentiating the vertexes from the edges... Read More
    • Mathematical Induction
      In Mathematical induction we find whether a given statement is true for all the natural Numbers or not. So the answer to What is Mathematical Induction is that it is basically a technique used to prove a statement or a theorem, or... Read More
      • Proof of Mathematical Induction
        In simple terms Proof of Mathematical Induction is a process typically which is used for proving of the Math statement which is true for all positive integers. Perhaps we must not get confused with the proof by mathematic... Read More
      • Recursion
        Recursion is the process of repeating it-self in its own way. The term is very vast and has many implications. If we are taking about practical implementation of recursion we can take two parallel mirrors facing each other, now we will see so ... Read More
    • Principle of Counting
      While dealing with the recurrence function we have to solve the function with different methods and approaches and we also apply some principles to solve them, here we have the basic principle of counting. That is if we have p ways... Read More
  • Trigonometry

    Trigonometry is that branch of mathematics which deals with the real life problems related to angles. Trigo means three sides, so trigonometry is basically a branch of mathematics which relates to the study of three sided figures i.e. tri... Read More

    • Inverse Trigonometric Functions
      The inverse Trigonometric Functions are partial inverse Functions for trigonometric functions.
      Now we will see the representation of inverse trigonometric functions:
      Function        Inverse
      Sin                arcsin
      C... Read More
    • Graphs of Circular Functions
      The equation x² + y² = 1 forms the Circle in Rectangular Coordinate System. This graph is known as Unit Circle it has radius one with the center at its origin i.e. (0, 0). The Domain of the trigonometric function is the Set ... Read More
      • Changes in Sine and Cosine Functions
        Sine and cosine Functions are Circular Functions or we can say they are trigonometric functions. Here we will discuss Changes in Sine and Cosine Functions. Sine function is a trigonometric Ratio which is equals to ra... Read More
  • Algebra

    Algebra is an important branch of mathematics in which we deal with several types of problems. These problems may either related to constants or variables. It is an interesting part of Math, and in this we mainly concentrate on "how to solve Numb... Read More

    • Algebraic Numbers
      A number which is root of a non – zero polynomial with rational coefficients is known as algebraic number.
      For example: If we have a polynomial
      ⇒3p² – 4p + 2 = 0; then ‘p’ is algebraic number because it is a non- zero Polynomials and... Read More
    • Linear Programming
      Linear programming is abbreviated as LPP is a mathematical process of linear optimization. Linear programming Definition says that it is used to determine maximum profit or minimum cost or minimum profit or maximum cost out of list of... Read More
    • Graphing and Functions
      As we know that in a function each input value is instantly lined with one corresponding output value of that function. General concept of a graph is characterized by graph of relation. A function is always recognized by its graph... Read More
      • Common Graphs
        Graphs can be defined as plot of any expression or we can say representation of an expression on a graph. Here we will see some Common Graphs. Some common graphs are line graph, Parabola graph, Absolute value graph, Cubic graph, Square Roo... Read More
  • Algebra 1

    Algebra 1 is part of algebraic mathematics which can be define as Algebra 1 is a branch of mathematics in which we represent the components of a specified Set or the numbers by use of symbols, alphabetical letters to express general relation... Read More

    • Money Math
      Addition, subtraction, multiplication, division and various mathematical operations are used in money Math Problems. For example, we went in a mall and purchased two jeans and 2 shirts and it costs us $ 3032.35. We don’t have change in return... Read More
  • Algebra 2

    Algebra 2 consists of many topics which are especially included for students who are weak in maths as they are quiet easy. The topics under Algebra 2 are:

    1.  Equations and inequalities which consist of many principles like:

    Adding p... Read More

    • Exploring Rational Expressions
      We know that all the mathematical operations can be performed on the Rational Numbers. We say that the Rational expression is the Mathematical Expression in which we can find the rational numbers combined together with the... Read More
    • Solving Systems of Linear Equations and Inequalities
      When we plot a graph then if equation makes a straight line then the equation is known as linear equation. For example:  y = mx + c; where ‘m’ is the Slope of a line and ‘c’ is Y- intercept where the ... Read More
    • Using Matrices
      Matrices are a Set of Numbers or we can say it is a collection of number which is arranged in rows and column. The numbers which we are using in matrices are Real Numbers. Generally in the matrices the complex numbers are used. With the h... Read More
    • Exploring Polynomial Functions
      Any polynomial function is said to be an expression of the form p(x) = a₀ + a₁*x + a₂ * x² + a₃* x³ . . . . + a_n * xⁿ , where we have a_n< > 0, is called the polynomial Functions, ‘x’ in the degree of ‘n’. While exploring p... Read More
    • Exploring Polynomials and Radical Expression
      An expression which consists of constant, variables and exponent values is known as polynomial expression. The polynomial expression is combined with the addition, subtraction, and multiplication.
      Like 5x² +... Read More
    • Graphing Linear Relations and Functions
      A Set of Ordered Pair is known as relation.
      Suppose we have (2, 5), (-3, 4), (12, -5), (5, 7), (0, 5), (6, 9), (1, 6);
      The value lies on x – axis and it is known as Domain of given set and the value of y – axis ... Read More
    • Investigating Sequences and Series
      Three types of sequences are there i.e. A.P. (Arithmetic Progression), G.P. (Geometric Progression) and Harmonic Progression (H.P.), here we will be investigating sequences of these three types.
      Progression is defined... Read More
  • Precalculus

    Precalculus is a vast concept as it covers large number of topics and other concepts. Precalculus does not include topics from Calculus but it covers the topics and concepts which will be useful in calculus. Precalculus is studied from pri... Read More

    • Exponents and Logarithms
      In mathematics, logarithm is a function or a power function which is used to increases the number logarithmically. The Logarithm of 10000 to base 1000 is 4, because 10000 are 10 to the power 4.
      We can also write as: 10000 = 10 ... Read More
    • Rational Function
      Ratio of two polynomial Functions is defined as a rational Function, where, a Polynomial is a finite length expression, made up of 3 basic mathematical operations( addition, subtraction and multiplication and non-negative exponents) wh... Read More
    • Scalar
      Scalar Math is studied in linear Algebra where real number is considered as scalar and we can also relate the term scalar math with the vectors in vector space by using the operation known as Scalar Multiplication. In this operation a scalar or a... Read More
    • Parametric Equations
      In plane, parametric equation is a pair of Functions which is given by:
      ⇒x = f (s) and y = g (s); which is used to define the ‘x’ and ‘y’ coordinate graph of the given curve in the plane.
      In mathematics, a Set of equations which i... Read More
    • Asymptote
      An asymptote is basically a line in which a graph approaches, but it never intersects the line. For example: In the following given graph of P =1 / Q, (here the x axis is denoted by ‘P’ and y axis is denoted by Q) the line approaches the p-axi... Read More
    • Precalculus Functions
      In Precalculus we study many topics which are Sets, real Numbers, complex numbers, composite and polynomial Functions, trigonometry, limits, vectors, metrics,  conic section, logarithm function, basic graphs, binomial theorem, math... Read More
    • Spherical Coordinates
      In three dimensional spaces Spherical Coordinate is used to find the location of a Point that depends on the distance ρ which is measured from the origin and two angles θ and ϕ. When we are going to define a spherical coordinate s... Read More
  • Calculus

    Calculus! many students get fear with this branch of mathematics as it is consider as one of the difficult branch of Math. The word Calculus is derived from Latin word, which means calculating something and used for counting anything. Calculu... Read More

    • Differential Calculus

      When we talk about study of differential calculus, our primary objective is to study about the Derivatives of the function. Differential Calculus is the important part of calculus, in which we deal with the change of rate of quan... Read More

      • Differential Equations

        Differential equations are those types of equations that have some Derivatives of certain Functions. The derivatives can either be ordinary derivatives or partial derivatives. If there are only ordinary derivatives in the equati... Read More

        • Second Order Linear Differential Equation

          When we calculate rate of any function with respect to any variable, then this procedure is called as a differentiation. For example y = f(x), then if we differentiate y with respect to x, it produces dy/dx, ... Read More

        • Higher Order Linear Differential equations

          Differentiation is important and interesting part of mathematics. We use differentiation process for calculating the rate of particular function with respect to particular variable like f(x) is a function an... Read More

        • Qualitative Solutions to Differential equations

          In differential equation we study the equations which are changed when their parameters changed or it is the study of anything that changes. From the study of differential, we learn that the derivative ... Read More

      • Application of Differentiation

        The differentiation is the subfield of Calculus and there are various application of differentiation in real world. The differentiation is very important part of Math as it is used in many scientific fields. Differentia... Read More

        • Slope, Length and Area for Polar Curves

          Slope, length, area for polar curves in Calculus is one of the most interesting and bit complex topic of Calculus. In this section, we will look at areas enclosed by polar curves. Here, we used the word “enclose... Read More

      • Maxima and Minima

        Maxima and minima of a function together can be called as extrema. Maxima and minima can be defined as largest and smallest of a function at a given Point in its Domain or outside its domain. We can calculate the maxima and minima o... Read More

    • Derivatives

      The derivatives are the measure of the function that how a function changes as function’s input changes. In short derivatives Calculus describes the behavior of one function in accordance with the other function. In calculus derivatives e... Read More

    • Integration

      Integration is widely used in sociology, economy, mathematics, electronics engineering and many other fields. Here, we will discuss integration in terms of mathematics, which is called as integral Calculus or integration calculus. In math... Read More

      • Fourier Series and Laplace Series

        In Fourier series and Laplace series first we will discuss about the topic of Fourier series, and later we will go on laplace series, Fourier series was formulated by a Jean-Baptiste Fourier. he showed that an imagin... Read More

        • Laplace Transform

          Laplace transform comes under integral transform that is used in so many areas of mathematics applications that relates to physics and engineering. Laplace transform check’s a function and if modification is require than changes in ... Read More

          • Formal Definition of Laplace Transform

            Laplace is widely used integral transform in the mathematics. Laplace transform of a function f (t) denoted by Lf)t) and its related Fourier Transform. 

            Definition of Laplace Transform is as follows:

            F(s... Read More

          • Properties and Theorems of Laplace Transform

            Laplace Functions can easily be solved with help of Laplace properties. Laplace transform properties are given below:

            1. Linearity: All the Laplace function fallow linearity property as:

            kx1 (t) +m... Read More

            • Relationship to Laplace Transform to other transform

              Laplace transform rechecks a function into its instance. Relationship of Laplace Transform to other transform can be given  as:

              Laplace transform performs on the density of function of measure ... Read More

      • Differential Equations and Mathematical Modelling

        A mathematical model for any system is the description of that system which uses the mathematical concepts related to the differential equation and some of the languages. This process of modeling is c... Read More

        • Exponential Growth and Decay

          Exponential growth and decay are some of the real world problems and it includes all those problems which increases or decreases exponential. Generally the exponential growth of any mathematical function occurs when the g... Read More

    • Application of Integration

      Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related to the definite integrals... Read More

  • Probability and Statistics

    Probability theory provides a structure or model of certain real world situations that provide very useful understanding and insight about making predictions.
    Here we are talking about the Statistics in mathematics. Statistics is the collecti... Read More

    • Probability

      In statistical mathematics we perform various tasks to accomplish the calculations which are related to the possibility of the event. In general aspect probability is used to describe the process of behavioral or logical estimation, which dep... Read More

      • Limit Theorems
        Limit theorems in Probability are useful for solving the complex Probability and Statistics problems. Here we will discuss some important limit theorems used in probability and statistics:
        There are following limit theorems in probabilit... Read More
      • Markov Chains
        Let us talk about Markov chain introduction. Markov chain is a system in which one state undergoes transitions to another state where states are always in the countable form. It’s the random process in which the next state does not depend ... Read More
    • Statistics

      Statistics is one of the very important and useful fields of mathematics. In statistic we study how to do the collection of data, then how to organize, analyze and interpret data. It is simply concerned with all these things and also involves ... Read More

      • Curve Fitting
        It is easier to understand the graphical view rather than mathematical view, that’s why curve fitting Statistics is useful in statistics, curve fitting statistics is a way to represent large number of data in the form of curve. Proper defi... Read More
        • Linear Function
          Calculus is based upon the linear Functions. Linear Functions are the functions whose graphs consist of sections of one straight line throughout the function's Domain.
          Linear function Statistics can be defined as the functions that have... Read More
    • Poisson Process
      A Poisson process is a random process that counts the number of events occurring and the time interval within which the events have occurred . The time between the two consecutive or back to back events is exponentially distributed ... Read More