My books and research articles

 The books you will see below, I wrote after seeing the needs of my students. Currently they are available in Spanish university libraries, and the rest of the world. You can find them in Spain (indicating my name or my last name) using the union catalog REBIUN, or other catalogs of other communities as CBUA or CCUC. And to find them in universities abroad, you can search at the WorldCat. These books can be ordered directly through the publisher's website, or in any bookstore (including online bookstores such as Amazon ). Likewise, the research articles are shared in Academia.edu and Researchgate.net, and some of them are being reviewed in a mathematical journal.

Books:

Linear Algebra I

Linear Algebra I is a book for university students of any university branch of science. You will find summaries of theory and exercises solved, of the following topics: Matrices, Resolution of Linear Systems Equations, Vector Spaces, Linear Transformations, Diagonalization of endomorphism, and Bilinear and Quadratic Forms.

Calculus I

Calculus I is a book for university students of any university branch of science. You will find summaries of theory and exercises solved, of the following topics: Real Numbers, Complex Numbers, Basic Topology, Sequences, Series, Functions:Limits and Continuity, Differential Calculus, and Riemann Integral.

Descriptive and Inferential Statistics

Descriptive and Inferential Statistics, is a book that is intended for university students of any college. You'll find theory as summaries, and exercises solved, on the following topics: Descriptive Statistics, Confidence Intervals and Test Hypothesis for means, proportions and variances for one sample, Chi Square Test, Test Hypothesis for means, proportions and variances, for two or more samples, and Regression line. Statistical software such as SPSS, Minitab, programs have been used in the resolution of problems and in some cases have been resolved by using the Excel and also manually.

Applied Multivariate Statistical

Applied Multivariate Statistical Analysis, is a book that is intended for university students of any college. You'll find theory as summaries, and exercises solved, on the following topics: Multiple Linear Regression, Principal Component Analysis (without and with Varimax rotation), Analysis of Hierarchical Cluster, Discriminant Analysis, and Single and Multiple Correspondence Analysis. The Minitab Statistical package, have been used in the resolution of problems.

Psychometrics

This book is intended for university students who are studying a degree in psychology, and also for professional psychologists who wish to improve the techniques of validation of a test. It contains techniques of the Classical Theory Test, Item Response Theory, with examples of the application of each technique. The CTT includes validation techniques using Principal Components Analysis, Unidimensionality of Scales (among others), calculation of Coefficients of Reliability, calculation of indices related to the items (difficulty, discrimination), etc. And with respect to the IRT, you will find models for dichotomous items (such as the Rasch model), and models for polytomous items.

Maths from low to high level - Exercises solved

This is a book where you will find many solved exercises about Algebra, Linear Algebra, Calculus and Mathematical Analysis. It is very useful for all those students needing help and support. The exercises are solved step by step, explaining how and why the exercise is solved by this way. It's not a theory book. And you will find exercises about: equations, numbers satisfying any conditions, non linear system equations, vectors and algebraic geometry, integral domains, Diophantine equations, linear algebra, absolute value, inequalities (any of them using absolute value), limits, continuity, function domain, derivable functions, study of a function (maximum, minimum, increasing and decreasing intervals, concavity), series and integrals (any of them using Beta and Gamma functions).

Proof of Fermat's Last Theorem

A historical theorem finally proved by Andrew Wiles. He deserves all my deepest respect and admiration. I also extend this admiration and respect to all mathematicians of today and yesterday. I graduated in Mathematics from the Autonomous University of Barcelona since 1988. Currently I’m a teacher of different mathematics subjects at university level. During these years, I have published many books. These books are available around the world in university libraries and also in any bookstore. This book is a bit different from the previous ones, as it presents the discovery of what could be a surprisingly simple proof of Fermat's last Theorem. I developed this demonstration in 1998, but I never thought to disclose it until now. And I've decided to disclose it now because someone recently reminded me that it was kept in a drawer, and perhaps the world should know.

Statement and Predicate Logic

This book is intended for university students, the scientific branch and even philosophy. It contains summaries of theory and exercises solved. In particular: how the connectives and quantifiers are used to formalize reasoning and statements, and how to use the methods of natural deduction, resolution, and truth tables, to validate whether or not a reasoning is correct. We often use the word "logic". In day to day, we express opinions because of information that they have. These opinions on logic are "conclusions", and the informations are "premises". But your opinion is always right?, or, some information is not completely true, or it is not expressed properly, and your opinion is wrong?. Sometimes our rational mind deceives us, happens that what seemed certain it is not true, and what it seemed impossible it is true. They say that the scientific world, is not
distant of the philosophical and artistic. And it is true. All is an art.

Fermat equation over several fields and other historical mathematical conjectures

As a teacher of several mathematics subjects at university level, and writer of several books that preceded to this one, and as a result of my goal to try to explain what seemed difficult as something easy, for a few years I began to investigate in several mathematics areas about possible simple proofs to complex mathematical problems. This book contains the results of these investigations, referring to Fermat's last theorem, as well as the existence of solutions for the Fermat equation in other fields such as quadratic integers and Gaussians, and conjectures such as Collatz conjecture and Goldbach strong conjecture.

My first Sudoku

This book contains Sudokus for children, with geometric figures of different colors. Each Sudoku also has its solution. A fun way to learn. The children use their logic with this book, and without realizing it, they also learn to differentiate the most common geometric figures. Interior of the book in full color.

My first Sums and Subtractions

This book contains sums and subtractions for children. With drawings of different colors, first we add apples, then pears, or bananas, or strawberries, and then we also subtract. A fun way for your child to start learning how to add and subtract. Interior of the book in full color.

My first logic games

This book contains logic games for children. With drawings of triangles, squares and circles, or with airplanes, cars and boats, or with stars, suns and moons, or with puppies, fish and sheep, or with the faces of a die, or with arrows, or with dots, or with the numbers from 1 to 9, or with some letters of the alphabet. In total it contains 10 games, each set with 7 logical series. Each game has its solution. A fun and entertaining way for your child to develop the logic.

Research Articles:

Fermat Last Theorem

 Fermat last theorem proof using classical geometry In Researchgate.net In Academia.edu

Goldbach strong conjecture

 Goldbach Strong Conjecture proof using induction mathematical method In Researchgate.net In Academia.edu

Collatz conjecture

 Collatz Conjecture proof using induction mathematical method In Researchgate.net

Extension of FLT in Gaussians integers for n>2

 Proof: There is no solution of FLT in Gaussians integers for all n>2 In Researchgate.net

Cubic Fermat equation in other fields

No solution in gaussian integers
In Researchgate.net
No solution in all  quadratic integers
In Researchgate.net
Solution in quadratic integers - A. Aigner
In Researchgate.net
Solution in quadratic integers in non conjugate form
In Researchgate.net
Solving the system equations to find quadratic integers solution
In Researchgate.net
There are infinite Fermat numbers no prime
In  Researchgate.net
There are infinite twin primes numbers
In  Researchgate.net

Value of the golden ratio (number Phi) knowing the side length of a square

 Value of the golden ratio (number phi) knowing the side length os a square In Researchgate.net

EC3 Project

 Management of Big Textual Data in Qualitative Research: Organizing the relationships in a typology based on logical properties In Researchgate.net In ACM Digital Library How to extract knowledge of Qualitative Data from Big Textual Data In Researchgate.net In SCIREA Journal of Computer

Alpine Landscape

 Descartes Project Spanish Royal Mathematical Society The paradise of mathematics Wit Games Club Mensa WIRIS your calculator on the Web

(c) 2011 Mercedes Orús Lacort   Author: Mercedes Orús Lacort
mercedes.orus@gmail.com