
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
Goldbach strong conjecture
Collatz conjecture
Extension of FLT in Gaussians integers for
n>2
Cubic Fermat equation in other fields


Links
of interest
Alpine Landscape
