Description:
~Mathematics as a subject is so serious that no opportunity should be missed to make this
subject more entertaining. (Blaise Pascal)
subject more entertaining. (Blaise Pascal)
Even today, it is said to happen from time to time that someone picks up a book in a quiet
hour to browse through it; however, in the rarest cases this will be a mathematics book, but
this is not so much due to the mathematics itself, but to the way it is presented in many
books. If terms like “dry”, “brittle” or “incomprehensible” come to mind here, we are
already well on the way to a common assessment.
Unfortunately, mathematics has a high “yuck” factor in society, and this is often due to
traumatic school experiences and bad textbooks for students. With such a school career,
however, one is usually afraid of the mathematical parts of studies, and quite in the spirit of
a self-fulfilling prophecy, one then really gets into trouble there.
With this book, we try to save you from these entry problems by building a bridge in an
entertaining way that gently guides you over all shoals into the interior of college
mathematics. This bridge starts on one side with simple number crunching, as you probably
encountered it in middle school, and takes you across to the basics of linear algebra,
differential calculus, and probability, which will be the main content of your first semesters.
You will always face this content there, and when dealing with it, you can then say with
confidence, “I know it already!”
The book is aimed at students of all disciplines who come into contact with mathematics
in the course of their studies or even their professional lives. One of our main concerns is to
prove that it is possible to write a mathematics book that is easy to read from cover to cover
without getting lost in formalism or humourless dryness, but which, after reading, has
nevertheless given you the necessary knowledge and technical confidence for a successful
mathematics part of your studies.
A large number of exercises, the solutions of which you will find at the end of the book,
will help you to further deepen what you have read. We have deliberately avoided proofs
for the most part – you will have to deal with this often enough in the course of your
studies – rather, we simply want to whet your appetite for mathematics, even if this may
seem contradictory to you at the moment.
A major annoyance in our eyes is the “nurse plural” displayed by many textbook authors
(“How are we doing today?”, “So tomorrow we’ll have our livers out!”, “Now let’s
integrate a function!”). Horrible! (Mind you, this refers only to this formulation bad
habit, not to the profession of nursing, a group whose representatives each individually
probably do more for humanity than all the mathematics professors in the world put
together). In order to avoid this bad habit, we have decided to address you personally in
each chapter in first-person style – each of us has written those chapters whose contents he
can convey competently and (hopefully) instructively, and this should also be expressed by
the writing style.
And now (and we mean it!): Have fun studying the following pages!
hour to browse through it; however, in the rarest cases this will be a mathematics book, but
this is not so much due to the mathematics itself, but to the way it is presented in many
books. If terms like “dry”, “brittle” or “incomprehensible” come to mind here, we are
already well on the way to a common assessment.
Unfortunately, mathematics has a high “yuck” factor in society, and this is often due to
traumatic school experiences and bad textbooks for students. With such a school career,
however, one is usually afraid of the mathematical parts of studies, and quite in the spirit of
a self-fulfilling prophecy, one then really gets into trouble there.
With this book, we try to save you from these entry problems by building a bridge in an
entertaining way that gently guides you over all shoals into the interior of college
mathematics. This bridge starts on one side with simple number crunching, as you probably
encountered it in middle school, and takes you across to the basics of linear algebra,
differential calculus, and probability, which will be the main content of your first semesters.
You will always face this content there, and when dealing with it, you can then say with
confidence, “I know it already!”
The book is aimed at students of all disciplines who come into contact with mathematics
in the course of their studies or even their professional lives. One of our main concerns is to
prove that it is possible to write a mathematics book that is easy to read from cover to cover
without getting lost in formalism or humourless dryness, but which, after reading, has
nevertheless given you the necessary knowledge and technical confidence for a successful
mathematics part of your studies.
A large number of exercises, the solutions of which you will find at the end of the book,
will help you to further deepen what you have read. We have deliberately avoided proofs
for the most part – you will have to deal with this often enough in the course of your
studies – rather, we simply want to whet your appetite for mathematics, even if this may
seem contradictory to you at the moment.
A major annoyance in our eyes is the “nurse plural” displayed by many textbook authors
(“How are we doing today?”, “So tomorrow we’ll have our livers out!”, “Now let’s
integrate a function!”). Horrible! (Mind you, this refers only to this formulation bad
habit, not to the profession of nursing, a group whose representatives each individually
probably do more for humanity than all the mathematics professors in the world put
together). In order to avoid this bad habit, we have decided to address you personally in
each chapter in first-person style – each of us has written those chapters whose contents he
can convey competently and (hopefully) instructively, and this should also be expressed by
the writing style.
And now (and we mean it!): Have fun studying the following pages!
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