What is Matita?
(pron. matita) MAThematics In Teaching Aid; (Italian) pencil. Matita is a collection of university level mathematics lessons, in both Italian and English.

Matita is like a personal, hand-held tutor who can guide you to success on your next exam with clear explanations of mathematics.
What does it do?
Matita simplifies the learning of mathematics, making studying easier and faster. It provides an easily accessible and effective alternative:
Matita eliminates all of the pre-exam anxiety and uncertainty. If you have not succeeded in mathematics, Matita is the right tool for you.

Individual Matita lessons may be used as often as you wish until you develop a keen understanding of the material.
Who is it for?
Matita is intended for:
What is included?
Each individual lesson contains a set of resources dedicated to a specific topic and is independent of the other lessons. There are no purchase restrictions: you can purchase only the lessons you need, as a replacement for lessons you were not able to attend or as a learning supplement for topics in which you struggle.

The catalogue is always a work in progress and is regularly updated with new material. The lessons, available in both English and Italian, cost less than your morning coffee at Starbucks.

Basic mathematics for university. Let us do it!
The idea and the use of small-o and asymptotic symbols. Notable limits. Sequences. Continuity. Many exercises and hard-work on a fundamental argument.
Organize the study of a graph of a function in 1 variable. Apply limits and differential calculus to a huge amount of exercises and examples. Find your way through the theory learning how to practice.
Study of Functions - Pro
How to master with hard exercises in differential calculus for functions in one variable. Become an expert of the study of the graph : a step by step procedure from the domain to the representation.
Matrices are one of the key instruments in a scientific path. The world of linear algebra is conveyed through them. FREE LESSON
Linear Systems
Every applied science shows many models of linear systems like Ax=b. We focus on the consistency condition, explain techniques for solving them and discuss parametric cases.
Linear Functions
Every linear function between euclidean spaces is represented by a matrix. The rank of that matrix is crucial to describe the injectivity and the surjectivity of that mapping.
Eigenvalues and eigenvectors associated to a linear transformation and their properties. How to find them.
Spectral Theorem
Similar matrices. Diagonalization and orthogonal diagonalization.
Complex Numbers
Meet complex numbers with video tutorials and dozens of solved exercises. You will familiarize and expand your computational capabilities from the formal construction to the applications.
Taylor Polynomial
... and Maclaurin's polynomials are fundamental in applications! We use them in the calculations of limits and in estimating the error. FREE LESSON in progress What would you need? Write me!
Discover more
Each lesson is composed of video-lessons, exercises and video-exercises, a glossary and a notation guide.

The video is framed around the calculations and graphics, overlayed with the sound of a voice explaining each step as it is completed. The videos are carefully edited so you experience a fluid lesson.
From the lesson “Study of functions - Pro”

The topic is always approached from different points of view, to provide various entry points to achieve understanding. The calculations are emphasized, with detailed algebraic steps clearly illustrated. Additionally, geometric representations are provided, as they offer intuitive and accessible explanations of the underlying concepts.

The calculations are completed using only a pencil (Matita), often in different colors to aid in comprehension. Theoretical topics include necessary proofs, explained in a way that you will understand immediately.
Exercises and video-exercises
Is your mathematics workbook lacking in explanation? Be at ease, it is no longer needed. Each Matita lesson is accompanied by a rich collection of exercises and video-exercises, with both open-ended and closed response questions taken from university exams.
The solutions are presented with all the calculations completed carefully and clearly, and no steps are omitted. Unlike your workbook, Matita takes nothing for granted.

The exercises are sorted by difficulty level: from the simplest to the more complex. You can select the exercises at the appropriated level to optimize your training.
Are your math notes lacking in clarity? Are you unclear about a particular theorem? Look no further. Are you completing an exercise and don’t remember a formula? Use the Glossary as a quick reference for reviewing the definitions and topics presented in the lesson, as an easy alternative to searching endlessly in your textbook.
Notation Guide
This section contains a legend complete with all the expressions and symbols used in the lessons, and their meanings. It will help you gain familiarity with with the conventional language of mathematics and give sense to the symbols.
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The author
Who am I?
My name is Federico, but my students call me Professor Vegni.

Teaching mathematics is my passion. I am currently teaching courses at Polytechnic University and Bocconi University (in Milan, Italy). With a Masters degree in engineering, a PhD in mathematics and many years of university teaching experience, I am well aware of the needs of students with majors in applied fields. (Download my CV).

My goal is not simply to give a lesson. I aim to deliver mathematics clearly and understandably, making it accessible for all. I am happy when I have captured the attention and the light above a student’s head flicks on.

I have many other life interests, including yoga (mainly Vinyasa, under Gabriella’s guidance) and theater. I have even performed in plays and assisted in theater productions. After all, teaching is quite similar to the theater: there is a stage, there are monologues and no audience likes to be bored :-)

P.S. When studying mathematics, I have always performed calculations by hand. I have found that this approach enhances my ability to both learn and teach the material. By the end of your first lesson, you will find this colorful technique to be quite effective.
Read my reviews
  • «Fra i migliori professori del Politecnico».
  • «Uno dei migliori professori che io abbia mai incontrato nella mia carriera studentesca, … si vede che insegna per il piacere di farlo».
  • «Il bilanciamento fra teoria e pratica è perfetto».
  • «Pragmatico, pratico e chiaro».
  • «Lezioni chiare, esaustive e coinvolgenti ed esercitazioni molto utili ed esplicative. … Tutto ciò unito a una voce rilassante e a un piacevole accento».
Review of my courses in Mathematical Analysis 1 and 2, Mathematical Analysis and Geometry posted on Unishare.it, an online platform for students to anonymously share their opinions of more than 3000 university courses taught in Italy.
  • «Il professore spiega in modo chiaro e preciso anche i concetti più difficili. Le esercitazioni, che risultano molto interessanti, sono ben strutturate e mai pesanti, data la bravura del prof. Vegni nello spiegare e nel far capire».
  • «Un corso meraviglioso, ti fornisce degli strumenti dell’analisi che ritorneranno utili in molti altri esami».
  • «Vegni è uno dei pochi che mantiene un certo ordine mentre scrive alla lavagna».
  • «Vegni non era il mio professore, ma ho seguito il corso con lui in quanto dal mio professore non si capiva nulla. È estremamente chiaro, preciso, ordinato, … se non avessi seguito lezione con Vegni non avrei passato il corso».
Review of my courses in Mathematical Analysis 1 and 2, Mathematical Analysis and Geometry posted on Unishare.it, an online platform for students to anonymously share their opinions of more than 3000 university courses taught in Italy.
  • «Definitely the professor. Professor Vegni clearly made a huge difference by having a teaching method close to the students, not giving anything for granted, explaining slowly and clearly the contents».
  • «I consider myself extremely lucky for having Mr Vegni as professor of this course because he is an impeccable person and professor. He’s always been so clear in the lectures, providing multiple examples and explanations, he was always available to the students for more clarifications, even though everything was already so much clear».
  • «Professor Vegni’s notes are simply amazing and simple to read. Had it not been for his neatness and use of different colors and a good handwriting, I would have been lost».
Ratings posted in Teaching Evaluation Program. Summary of Students Observations and Suggestions for my English language course in General Mathematics at Bocconi University (2014/2015).
  • «Great teacher, well organized topics».
  • «Professor Vegni is super qualified and keen on math teaching. We will miss him».
  • «It provides solid bases for economics».
  • «Engaging, stimulating and clear. Mathematics module 1 has been the easiest course to follow thanks not to its simplicity but mostly to the professor's knowledge».
  • «Inspiring, interesting, useful».
Ratings posted in Teaching Evaluation Program. Summary of Students Observations and Suggestions for my English language course in General Mathematics at Bocconi University (2014/2015).
Questions? Concerns? Would you like to propose a topic for the next lesson or know when it will be available?
Email me