# Mathematical Biology (MATH 3250)

** Office Hours **

N615 Ross, M 10:00-11:00am

** Time and Place **

Winter 2018

MWF: 12:30-13:30

Ross S507

Some lectures will be in the Gauss Lab.

** Starting Jan 23, Weds lectures are in the Gauss Lab. **

** Description **

This course introduces the student to the mathematical modelling with applications to biology in related fields such as chemistry, ecology and health. There is an emphasis on case studies and problem solving skills. Topics include discrete and continuous models describing population dynamics, population health, chemical reactions and biological structures.

** Syllabus: ** found here pdf file

** Project Presentations: ** Due April 1 - post a video of your project presentation (10 - 15 minutes length) to a dropbox folder that will be emailed to you (for security). Please note that the folder only allows uploading and viewing - no revision is allowed.

** Project information: ** Sample proposal and outline pdf file

** Project Rubric: ** Marking scheme pdf file

** Project Peer Evaluation Form - Presentations: ** Marking scheme pdf file

Matlab refresher - Lab questions

Lab 1 - found here pdf file

Due Feb 1 - Submit your reflection papers on the papers handed out in class Friday Jan 25. Group presentations on Feb 1 should be 15 minutes long.

Lab 2 - found here curvefitting (open in Word, copy and paste into Matlab script) and predprey

Salmon example

clear;

A=[0 4 3; 0.5 0 0; 0 0.25 0]

startvec=[1;0;0]

for i =1:100

popvals(:,i)=A^i*startvec;

end;

popvals

for j=1:100

normpopvals(:,j)=popvals(:,j)./sum(popvals(:,j));

end;

normpopvals

[V,D]=eig(A)

domeig=max(max(abs(D)))

getposition=find(abs(D)==domeig)

domeigvec=V(:,getposition)

domeigvec./(sum(domeigvec))

checking=domeigvec./(sum(domeigvec))

cc=A*checking

cc./sum(cc)

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Lab 4 - Predator-prey models pdf file and maple file

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Lab 5 - we will anlayze our model for NHL expansion in the GTA

dS/dt = -S*YL*bLS-S*YO*bOS-S*d+YL*wL+YO*wO+lambda

dYL/dt = S*YL*bLS+YL*YO*bLO-YL*YO*bOL-YL*d-YL*wL;

dYO/dt = S*YO*bOS-YL*YO*bLO+YL*YO*bOL-YO*d-YO*wO;

See Maple file here - pdf_file

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Lab 6 - over email

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Lab 7 - Michaelis-Menten kinetics - pdf_file (worksheet done in class - pdf_file)

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Lab 8 - copy and paste the matlab code below

clear;

F1 = [0;0;0];

Layer1_weights = [0.8,0.4,0.3; 0.2,0.9,0.5];

Layer2_weights = [0.3;0.5;0.9];

wanted_output=0;

input_vars = [1;1];

F2_correction = 10;

threshold = 0.001

kk=1;

while abs(F2_correction)>threshold

H1(1) = sum(Layer1_weights(:,1).*input_vars(:,1));

F1(1) = 1/(1+exp(-H1(1)));

H1(2) = sum(Layer1_weights(:,2).*input_vars(:,1));

F1(2) = 1/(1+exp(-H1(2)));

H1(3) = sum(Layer1_weights(:,3).*input_vars(:,1));

F1(3) = 1/(1+exp(-H1(3)));

H2(1) = sum(Layer2_weights(:,1).*F1(:,1));

F2(1) = 1/(1+exp(-H2(1)))

F2_correction = wanted_output-F2;

outputF2_correction(kk)=F2_correction;

if abs(F2_correction)>threshold

Doutputsum= (exp(-H2)/(1+exp(-H2))^2)*F2_correction;

Dweights=Doutputsum.*F1;

Layer2_weights = (Layer2_weights+Dweights);

Dhiddensum = (Doutputsum.*Layer2_weights').*(exp(-H1)./(1+exp(-H1)).^2);

Dhiddenweights=[Dhiddensum*input_vars(1,:); Dhiddensum*input_vars(2,:)];

Layer1_weights=Layer1_weights+Dhiddenweights;

kk=kk+1

else

jjjjj=0;

end;

end;

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Genetics notes - pdf file

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Assignment 1 - pdf file

Assignment 2 - pdf file