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- The answer is going to be quite long and comprehensive, read till the end, its worth it:
- See, Math is divided into the following 8 parts. Don’t rush to do all overnight, you’ll get demotivated and lose interest. Rather do it module wise, in chunks that you can chew, Its like going 0 to hero in this order:
- Module 1: Basics and Algebra
- Module 2: Pre-Calculus
- Module 3: Calculus
- Module 4: Transformations
- Module 5: Mathematical Logic
- Module 6: Graph Theory
- Module 7: Algorithms
- Module 8: Cryptography
- Module 1: BASICS AND ALGEBRA
- Understanding number theory, what are real numbers(rational, irrational, fractional, integer number, odd number, even number, prime number, co prime numbers, relatively prime numbers) what are complex numbers(rectangular form, Argand Diagrams, Polar Form, Exponential Form, De-Moivre’s Theorem).
- Understand what algebra is, read the fundamental rule of algebra(Fundamental theorem of algebra - Wikipedia), Learn how to solve linear simultaneous equations using substitution, elimination and cross elimination method. Then shift to quadratic equations, how to solve them using prime factorization, quadratic formula (Quadratic formula - Wikipedia), completing the square method(Completing the Square). Then move to higher degree equations, learn the synthetic division method (Synthetic division - Wikipedia) to factorize them.
- Move on to set theory (Set theory - Wikipedia), learn what are sets, subsets, power sets, cardinality of a set. After that learn basic set operations like union, intersection, set difference, complement. Learn how to represent sets as Venn diagrams. Learn about the inclusion - exclusion principle(Inclusion–exclusion principle - Wikipedia). Learn what are cartesian product of 2 sets, learn how relations are derived from cartesian products, learn how
- Move on to Matrix Algebra and learning what’re determinants are, and all the operations done on them (https://en.wikipedia.org/wiki/Ma...)
- Module 2: PRE - CALCULUS
- Learn about arithmetic progressions (Arithmetic progression - Wikipedia), geometric progressions(Geometric progression - Wikipedia).
- Learn What a Logarithm of a number is, what is Anti - Logarithm, what is the difference between common log and natural log. Learn how to read Log Tables.
- Move on to read and understanding what are Co-Ordinate geometry in 2 - D, understand what is an abscissa and an ordinate, know about the distance formula, the section formula, collinearity conditions in that order.
- Learn about Statistics, collection of data and sorting them into meaningful relationships by the use of histograms, frequency tables, etc. Learning what is univariate data. Then learning about the concepts of central tendency in a given data set and the ways to achieve it by making the use of Arithmetic Mean, Geometric Mean, Harmonic Mean, Median, mode, standard deviation, mean devaition.
- Learn about Co-Relation and Regression, how multi-variate data is represented and how are they related, Learn about karl pearson coefficient of correlation, Spearman ranks, etc.
- Learn the concept of a factorial of a number, learn what are permutations, combinations and derangements. Learn about the the Binomial Theorem as it is very useful.
- Next learn about, 3-D geometry: Intercepts, Slope of a line, Direction Ratios, Direction Cosines.
- Learn what are Vectors, Learn about Unit vectors, Learn about the dot and cross products.
- Next learn what is Linear Programming, how to optimize(either maximize or minimize)data sets using graphical and simplex methods.
- Learn about Probability next, probability of an event, probability of a negation of an event, what is a sample space, the standard layout of 52 poker cards, the Bayes theorem for conditional probability. Learn about discrete and continous probability. Learn discrete probability distributions like the Binomial, Geometric and the Poisson Distributions and continuous probability distributions like the Exponential Distribution.
- Next move on to read what exactly is trigonometry, what re trigonometric ratios of a right angled triangle, learn some basic values of trigonometry at standard angles like (0 deg, 30 deg, 45 deg, 60 deg and 90 deg). Learn about the ASTC system and shifts and periodicity of trigonometric ratios in all 4 quadrants. Inverse Trigonometry
- Module 3: CALCULUS
- Move on to Differential Calculus, learn the basic rules of differentiation, quotient rule, product rule, chain rule, parametric differentiation and all the derivatives of standard functions.
- Move on to Integral Calculus, learn that integration is just the opposite process of differentiation. Knowing what is an indefinite and definite integral. Learn the integrals of standard functions, Learn the substitution rule for integration next and the Bernoulli’s Generalized rule of integration by parts when you got to find the integral of the product of 2 functions. The concept of odd and even functions.
- Next, move on to Linear Differential Equations, learn the 4 methods to solve a differential equations that is, Variable Separable, Homogeneous Differential Equations, Bernoulli’s Differential Equations, Exact Differential Equations.
- Move to Higher Order Differential Equations, learn how to make an auxiliary equation, finding the complementary function (C.F) from that, and the particular integral using any of the 2 methods which are: Methods of Undetermined Coefficients or Method of Variation of Parameters.
- Next move to Partial Differentiation, which differentiating wrt one variable while keeping others constant.
- Learn the Leibniz nth derivative formula(General Leibniz rule - Wikipedia) next.
- Module 4: TRANSFORMATIONS
- Learn about Laplace Transformations and Inverse Laplace Transformations.
- Learn properties of Z-Transforms and their operations.
- Learn Fourier Series and Fourier Transforms.
- Learn Numerical Methods Like “Regula-Falsi and Newton-Raphson Method” .
- Module 5: MATHEMATICAL LOGIC
- Start with Basic rules of Logic, like: Commutative law, distributive law, absorption law, idempotent law, law of negation, De-Morgan’s Law.
- Learn Rules of Inferences like: Rule of conjunctive simplification, disjunctive amplification, transitive properties, Modus Ponnes, Modus Tollens.
- Learn about Open Statements/Quantifiers.
- Learn about the Pigeon-Hole Principle.
- Learn about First Order and Second Order Recurrence Relations.
- Module 6: GRAPH THEORY
- Move over to Trees, learn what is a tree, tree terminologies like(what is a root node, edges, siblings, child node, parent node, ancestor, leaf node, level of a node, height of the tree, depth of the tree), what is a binary tree, full binary tree, almost complete binary tree, Tree traversals like: Inorder, Preorder and PostOrder Traversals.
- Move on to graphs, learn what a graph is, learn graph related terminologies like: (vertex, edge, path, loop, multiple edge, indegree, outdegree of a node). Learn what’re Undirected, Directed and Weighted Graphs, Bipartite and Complete - Bipartite Graphs. Then learn about the transitive closure of a graph (Warshall Algorithm), learn how to represent a graph using adjacency matrix and adjacency list. Learn graph traversals like Depth First Traversals and Breadth First Traversals. Learn the Handshaking Property of a graph. Learn about the Konigsberg Bridge Problem.
- Learn what’re Prefix Trees and how to do derive Huffman Codes From that, next study what are Huffman Trees/Weighted Trees.
- Module 7: ALGORITHMS
- Learn how do the classify algorithms: Brute Force, Divide and Conquer, Decrease and Conquer.
- Learn Sorting Algorithms like: Bubble, Insertion, Selection, Merge, Quick and the Radix Sorts.
- Module 8: CRYPTOGRAPHY
- Learn the origins of cryptography, learn about the Caesar Cipher, then learn what is encryption. Learn what is decryption. Learn the difference between Symmetric Key and Asymmetric Key Cryptography.
- Learn how to generate prime numbers using Sieve of Eratosthenes method, Fermat’s Primality Test and the Naive Method.
- Learn Symmetric Key Algorithms like: The DES and the AES algorithm.
- Learn Asymmetric Key Algorithms like: The RSA Algorithm, The Diffie Hellman Key Exchange Protocols.
- Learn about Hashing Algorithms like the MD5 and SHA-1 algorithm.
- Lastly I would like to conclude by saying that math is a very interesting subject as it forces you to think instead of rote memorization of useless facts. Most people lose interest in math due to a bad teacher or other reasons. However don’t lose hope and try to be good at math, crunching numbers, visualizing relations in your mind.
- Math is everywhere you name it, Chemistry, Physics, Applied Math, Pure Math, Research, Fluid Mechanics, Signal Systems, Computer Networks, and yeah Google Search Engine, too.
- Learn how to use a scientific calculator, Buy a Casio FX-991 MS or FX - 991 ES.
- Gone are the days where you had to visit a library, Now in 2016 you can use the vast internet and there is YouTube channel called as Khan Academy just follow his videos.
- In the end, I just want to say, “Knowledge is power and comes to those who have a willingness to learn, experiment, think out of the box and persevere.”
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