PRINCIPLES OF MATHEMATICS 1

Obiettivi formativi

Principles of mathematics 1: The aim of this course is to give the student sound mathematical basis in calculus of one or several variables and optimization in a way appropriate for a student of bioinformatics. An emphasis is given to applications and intuitive understanding of the underlying concepts. The first semester (Principles of Mathematics 1) will be devoted mainly to the study of functions of one variables, including limits, derivative and integrals. Basic optimisation results for functions of one variable will also be considered Knowledge and understanding The aim of the course is to give students a basic understanding of calculus in a way appropriate to bioinformatics students. Students will also be exposed to mathematics proofs as an example of rigorous scientific reasoning. Applying knowledge and understanding By the end of the course, students will be able to use basic mathematical tools as applied to different environments. They will also be able to interpret in a critical way results obtained by applying mathematical modelling technique. Making judgements Lectures and practical exercises will provide students with the basic ability in assessing the main strengths and weaknesses of mathematical models when used to explain empirical evidence. Communication By the end of the course, students will have basic mathematical skills that will help them to talk in an appropriate way about quantitative models. Lifelong learning skills Students are expected to develop learning skills necessary to undertake additional and more advanced studies involving mathematics and mathematical modelling in biology. Principles of Mathematics 2: The aim of this course is to give the student sound mathematical basis in calculus of one or several variables and optimization in a way appropriate for a student of bioinformatics. An emphasis is given to applications and intuitive understanding of the underlying concepts. The second semester (Principles of Mathematics 2) will be devoted mainly to the study of functions of several variables, linear algebra, and differential equations. Basic optimization results for functions of several variables will also be considered. Knowledge and understanding The aim of the course is to give students a basic understanding of calculus in a way appropriate to bioinformatics students. Students will also be exposed to mathematics proofs as an example of rigorous scientific reasoning. Applying knowledge and understanding By the end of the course, students will be able to use basic mathematical tools as applied to different environments. They will also be able to interpret in a critical way results obtained by applying mathematical modelling technique. Making judgements Lectures and practical exercises will provide students with the basic ability in assessing the main strengths and weaknesses of mathematical models when used to explain empirical evidence. Communication By the end of the course, students will have basic mathematical skills that will help them to talk in an appropriate way about quantitative models. Lifelong learning skills Students are expected to develop learning skills necessary to undertake additional and more advanced studies involving mathematics and mathematical modelling in biology.

Canale 1
RENATO BRUNI Scheda docente

Programmi - Frequenza - Esami

Programma
1. Functions Sets, Intervals and functions. Types of functions. The graph of a function. Mathematical models. 2. Limits of a function. What is a limit. How to compute a limit. Laws of limits. Continuity of a function. Intermediate Value theorem; Bolzano's theorem. 3. Derivatives What is a differentiable function; the graph of a function; tangent in a point; geometric view of derivatives; local approximation to the function. Derivatives and properties of derivatives; meaning of positive and negative derivatives; examples. Fermat's Theorem; minimum and maximum points; Weierstrass' theorem; existence of minimum and maximum. Rolle's Theorem; Mean-value Theorem; computation of simple derivatives. 4. Integrals What is an integral; integrability of a function. Elementary properties of integrals; examples. The Fundamental Theorem of Calculus; practical computation of definite integrals. Indefinite integrals. Integration by substitution. Integration by parts.
Prerequisiti
Basic notions of mathematics, properties and operations on numbers (integers, rationals, reals, powers and roots, logarithms and exponentials), monomials and polynomials, literal calculation, algebraic equations and inequalities.
Testi di riferimento
Calculus For Biology and Medicine, author Claudia Neuhauser - Pearson 2014 Biocalculus: Calculus for Life Sciences, authors James Stewart, Troy Day – Cengage Learning 2015 Slides of the course, available from the home page of the professor (http://www.diag.uniroma1.it//~bruni/)
Modalità insegnamento
Lessons in Classroom Psicologia I and online with zoom at https://uniroma1.zoom.us/j/89314304070?pwd=YTJpZmlSS2pSV2N4b3dlN1lkZ1Z0Zz09
Frequenza
Lessons in Classroom Psicologia I and online with zoom at https://uniroma1.zoom.us/j/89314304070?pwd=YTJpZmlSS2pSV2N4b3dlN1lkZ1Z0Zz09
Modalità di esame
written exam
Modalità di erogazione
Lessons in Classroom Psicologia I and online with zoom at https://uniroma1.zoom.us/j/89314304070?pwd=YTJpZmlSS2pSV2N4b3dlN1lkZ1Z0Zz09
  • Anno accademico2025/2026
  • CorsoBioinformatics - Bioinformatica
  • CurriculumCurriculum unico
  • Anno1º anno
  • Semestre1º semestre
  • SSDMAT/09
  • CFU6