# Om emnet

Nytt fra studieåret 2022/2023

### Vurderingsordning

Vurderingsordning: Digital hjemmeeksamen
Karakter: Bestått/ Ikke bestått

Vurdering Vekting Varighet Delkarakter Hjelpemidler
Digital hjemmeeksamen 100/100 4 timer

### 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

After completing the course the student will:

• Have been exposed to basic constructive mathematical reasoning, including a very limited exposure to mathematical proofs.
• Have a familiarity with fundamental and ubiquitous concepts from Calculus including, but not limited to, the notion of functions, limits, continuity, derivatives and integrals.
• Have a basic understanding of how these concepts are applied to the resolution of problems involving minimization or maximization of a function and to the resolution of differential equations.
• Have a familiarity with basic ideas and concepts from Probability Theory.
• Be able to use this newfound knowledge to better understand the foundations of many analysis techniques widely employed in the Life Sciences.

### 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 be a digital home exam, which will contain exercises similar to the ones discussed during the course. The evaluation will be graded with pass/fail.

The students will be required to hand in 4 written assignments. The assignments will be evaluated as approved/not approved.

### Spesielle vilkår

Obligatorisk aktivitet fra tidligere semester kan godkjennes av instituttet.

### Forkunnskapskrav

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

### Kursmateriell

To be announced

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Versjon: 1
Studiepoeng:  7.5 SP

Undervisning

Termin nr.: 1
Undervises:  HØST 2022

Undervisningsspråk: Engelsk

Sted: Trondheim

Fagområde(r)
• Nevrovitenskap
• Algebra
Kontaktinformasjon
Emneansvarlig/koordinator: Faglærer(e):

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Kavliinstitutt for nevrovitenskap

# Eksamensinfo

#### Vurderingsordning: Digital hjemmeeksamen

Termin Statuskode Vurdering Vekting Hjelpemidler Dato Tid Eksamens- system
Høst ORD Digital hjemmeeksamen 100/100

Utlevering
27.01.2023

Innlevering
27.01.2023

09:00

13:00

Vår ORD Digital hjemmeeksamen 100/100
• * 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"

Mer om eksamen ved NTNU