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Natural Numbers

Natural numbers are those used for counting and ordering. We use numbers in our daily lives more often than we realize. Know more about natural numbers with us.

Natural numbers II

Natural numbers are those used for counting and ordering. Know more about natural numbers and how to learn basic arithmetic fast and easy.

Elementary Maths

Learn Math with us easily. We are talking about divisors, prime numbers, prime factorization, gcd, lcm, numeric systems, and more.

Learn Geometry with GeoGebra

GeoGebra is a free dynamic mathematics software and it is especially created for teaching and learning. Let's learn basic Geometry with Geogebra.

What is the best Maths software to learn and grow?

Do you have Maths homework? How do you know that your results are OK? This article is going to teach you how to use easy-to-use, free-of-charge software to check that your calculations are correct

Fractions are really cool!

A fraction is a fancy way of representing the division of a whole into parts. Learn fractions with us in a fun and engaging way.

Decimals, Percentages, Mixed numbers, and improper fractions

Decimals, fractions, and percentages are, basically, alternative ways of representing the same value. Learn fractions with us in a fun and engaging way.

Sets and Operations on Sets

A set is a collection of things or objects, such as animals, plants, vowels. Learn all about sets and set operations.

Polynomials, Equations, and Systems of equations

The step by step guide to learn everything that you need to know about polynomials, equations, and systems of equations.

Plotting functions

The step by step guide to learn everything that you need to know about functions and plotting their graphs.

Plotting functions II

The step by step guide to learn everything that you need to know about functions and plotting their graphs. Increasing and decreasing functions. Maximum and Minimum. Asymptotes. Convex functions. Data Visualization.

Statistics

A step by step guide to analyzing and interpreting data using LibreOffice Calc and R. R is a free programming language and statistical software for analyzing and visualizing data.

Statistics II. Chi-squared Test, ANOVA

A step by step guide to analyzing and interpreting data using LibreOffice Calc and R. Let's go deeper and study the Chi-squared Test of Independence, one-way and two-way ANOVA, and two-way repeated measures ANOVA.

Statistics III. T-tests, Correlations, Linear, and Multilinear Regression

This is the final article of a three-part blog series on analyzing and interpreting data. Today, we will learn about T-tests, correlations, lineal, and multilinear regressions.

Mathematical analysis

A brief, quick and dirty, introduction to Mathematical Analysis with Maxima, Python, and WolframAlpha. We will learn about functions, limits, derivatives, integrals, and series.

How to convert units

Unit conversion is the process of converting a quantity from one base or unit of measurement to another by multiplying or dividing it by a conversion factor.

How to use a calculator and how to measure objects

A calculator is a small electronic device or software application that can perform mathematical calculations. Screen rulers let you measure objects easily.

Complex Numbers

The easy-to-follow step by step guide to learn everything that you need to know about complex numbers. Learn to check the validity of your calculations with Octave, Python, and WolframAlpha.

Vectors, matrices, and system of linear equations

A step by step guide to learn everything that you need to know about vectors and matrices, as well as solving linear equations with many examples.

LibreOffice Math and LaTeX

LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. Python and LaTeX. Render LaTeX math expressions in Hugo

Calculus

Functions

Inverse Functions. Exponential and logarithms functions.

Limits

Precise definition. One-Sided Limits. Infinite Limits. Limits at infinity. The Squeeze Theorem. The Limit Laws.

Continuity and discontinuity

Definition and examples. What is a Discontinuous Function? Types of Discontinuity

Derivate

Definition and examples. Derivatives of Trigonometric, Inverse and Exponential and Logarithms Functions. General rules. Higher Derivatives. Implicit Differentiation

Sketching the Graph of a function

Increasing/Decreasing Functions. Concavity and inflection points. Asymptotes and End Behavior. Even and odd functions. General strategy to plot functions.

Applications of Derivatives

Maxima and Minima. Related rates. Newton's method.

Mean & Extreme Value, Fermat & Rolle.

Mean Value Theorem. Fermat's Theorem. Rolle's Theorem. Extreme Value Theorem. Boundedness theorem. The least-upper-bound property. Increasing and decreasing functions.

Antiderivates. Indefinite integrals.

Antiderivates. Indefinite integrals. Definition and Examples. Uniqueness of Antiderivatives.

Algebra

The Natural Numbers and induction. The Binomial Theorem.

The natural numbers. Mathematical induction. Strong Form of Induction. The binomial theorem.

Precalculus. Sets. Algebra of sets

Precalculus. Sets. Algebra of sets. Distributive Laws. Double inclusion. Cardinality.

Relations

Relations. Definition, examples, and properties. Equivalence relations. Partitions. Equivalence Classes Partition.

Functions or Mappings

Definition. Type of functions. Property of Functions. Cardinality of sets. Inverse functions.

Groups.

Bézout's identity. Definition and examples. Properties of Groups. Uniqueness of identity and inverses. Cancellation property.

Isomorphisms. Cayley's Theorem.

Homomorphism. Isomorphism. Cayley's Theorem. Properties of Isomorphisms. Automorphism.

Permutation Groups

Permutation Groups. Properties of Permutations. The Alternating Groups.

The dihedral group

The dihedral group. D4 is the symmetry group of the square. D3.

Cyclic Groups

Cyclic Groups. Definitions, examples, and properties. Classification of subgroups of cyclic groups.

Subgroups.

Subgroups. Definition and examples. Subgroup tests. Center of a Group. The Product HK of two subgroups H and K.

Cosets

Cosets. Definition. Examples. Properties of Cosets.

Lagrange's Theorem

Lagrange's Theorem. Corollaries. Classification of Groups of Order 2p. Orbits and Stabilizers.

Direct Products

Direct Products. Definition. Examples.

Resources

The Big Naughty List

Definition and examples. Derivatives of Trigonometric, Inverse and Exponential and Logarithms Functions. General rules. Higher Derivatives. Implicit Differentiation


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