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NEVR8015 - Math for Biologists II – Calculus and Introduction to Probability Theory

Om emnet

Undervises ikke studieåret 2024/2025

Vurderingsordning

Vurderingsordning: Skriftlig skoleeksamen
Karakter: Bestått/ Ikke bestått

Vurdering Vekting Varighet Delkarakter Hjelpemidler
Skriftlig skoleeksamen 100/100 4 timer B , E

Faglig innhold

Many fields within the Life Science are becoming increasingly quantitative and interdisciplinary. This poses the double challenge of having a good understanding of the biological aspects of the problem under study, as well as of the mathematics used to analyze the acquired data and to develop models for it. The goal of this course is to introduce PhD students in the Life Sciences to concepts in Calculus and Probability Theory that they will encounter in most of the analysis techniques and models they will employ in their research. The course will smoothly introduce the language of mathematics, with the aim of easing interdisciplinary communication. No previous mathematical knowledge is required, as we will start from the basics, namely: sets and functions. We will then introduce the concepts of limits and continuity of a function and build up from there to the concept of derivatives. We will see how to apply derivatives to solve optimization problems and to perform linear and higher order approximations of a function. We will then introduce the notion of (Riemann) integrals and connect them with the idea of derivatives via the Fundamental Theorem of Calculus. We will comment on how to extend these concepts to multivariate calculus, introducing the idea of gradients, and also on the application to differential equations. Finally, we will provide a short introduction to Probability Theory from the Bayesian perspective.

Læringsutbytte

Knowledge

After completing the course the student will possess knowledge of:

  • Fundamental concepts in Calculus and Probability Theory, including limits, derivatives, integrals, gradients, differential equations and the basic laws of probability.
  • The most important theorems and results in Calculus.
  • Introductory level material in Probability Theory

Skills

After completing the course the student will be able to:

  • Carry out simple mathematical proofs and follow along with more complex ones
  • Utilize mathematical notation and language to express their ideas more precisely.
  • Perform a number of calculations related to the topics of the course, such as calculating derivatives and simple integrals, perform polynomial approximations of a function, determine the solution to certain optimization problems and differential equations, solve simple probability problems and more.

Competence

After completing the course the student will be able to:

  • Understanding many of the basic elements employed in analysis techniques in the Biological Sciences, and being able to better interpret the results obtained with those methods, potentially recognizing their limits and how to go beyond them.
  • Applying mathematical reasoning and logic to better judge the validity of an argument.
  • Using the knowledge gained in this course to be able to approach more complex topics

Læringsformer og aktiviteter

Each class will be divided into a lecture and a practical session. The practical sessions will consist on solving exercises in order to assimilate the concepts introduced during the lectures. We will use the practical sessions to monitor the progress that the students make with the exercises. At the end of the course, and right before the exam, there will be a recap reserved for further discussion.

Obligatoriske aktiviteter

  • Obligatorisk oppgave

Mer om vurdering

The evaluation of the course will consist on a written exam, which will contain exercises similar to the ones discussed during the course. Additionally, students will be required to submit 4 short assignments throughout the course, which they will need to pass in order to be allowed to take the exam.

Forkunnskapskrav

The course is meant for PhD students working in the Life Sciences.

Kursmateriell

To be announced

Flere sider om emnet

Ingen

Fakta om emnet

Versjon: 1
Studiepoeng:  7.5 SP
Studienivå: Doktorgrads nivå

Undervisning

Ingen

Undervisningsspråk: Engelsk

Sted: Trondheim

Fagområde(r)
  • Nevrovitenskap
  • Algebra
Kontaktinformasjon

Ansvarlig enhet
Kavliinstitutt for nevrovitenskap

Timeplan

Listevisning
Kalendervisning

Eksamensinfo

Vurderingsordning: Skriftlig skoleeksamen

Termin Statuskode Vurdering Vekting Hjelpemidler Dato Tid Eksamens- system Rom *
Høst ORD Skriftlig skoleeksamen 100/100 B , E INSPERA
Rom Bygning Antall kandidater
Vår ORD Skriftlig skoleeksamen 100/100 B , E INSPERA
Rom Bygning Antall kandidater
  • * Skriftlig eksamen plasseres på rom 3 dager før eksamensdato. Hvis mer enn ett rom er oppgitt, finner du ditt rom på Studentweb.
Eksamensinfo

For mer info om oppmelding til og gjennomføring av eksamen, se "Innsida - Eksamen"

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