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Application: Kathleen WilkiePosting number: F326POPosting: Assistant Professor (Faculty / Academic Administrator / Unclassified)Form: Faculty ApplicationSubmitted: December 07, 2015 at 10:56 PM (confirmation number: CN000042492)

Personal Information

Personal Information

First Name: Kathleen

Middle Name:

Last Name: Wilkie

Address 72 Golden Ave

City: Medford

State MA

Zip Code 02155

Country United States of America

Primary Contact Number 781-866-0686

International Phone- Day

Extension

Alternate Contact Number 781-874-0728

International Phone - Night

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Email [email protected]

Are you legally able to work in the UnitedStates?

Yes

Will you require sponsorship by theUniversity to work or continue to work inthe United States?

Yes

Have you ever been convicted of afelony?

No

If No, Type N/A,If yes, describe thecircumstances of all convictions

N/A

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Kathleen Wilkie for Assistant Professor of 3

Page 55 of 122 | Created 12-11-2015 14:43:03 | Assistant Professor

Name of Reference Dr. Philip Hahnfeldt

Phone Number

Email Address [email protected]

How do you know this reference? Postdoctoral Advisor

Name of Reference Dr. Lynn Hlatky

Phone Number


How do you know this reference? Director of the Center for Cancer Systems Biology. Aware of bothmy research and my service to the field of cancer systems biology.

Name of Reference Dr. Sivabal Sivaloganathan

Phone Number


How do you know this reference? PhD supervisor

Name of Reference Dr. David McKinnon

Phone Number


How do you know this reference? Teaching Reference

Name of Reference Dan Wolczuk

Phone Number


How do you know this reference? Teaching Reference

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Certification Statement

I certify that the information given on this application is true and correct. I understand that any false information, willful ornegligent misrepresentation, or failure to disclose any requested information relating to the contents of this application willconstitute sufficient grounds for the University of Vermont to terminate my employment. I further understand that theUniversity will adhere to the provisions of all applicable laws, including whenever applicable, the Fair Credit Reporting Actconcerning securing, documentation, handling and release of information obtained in the pre and post employmentinvestigation. Employment contingent upon completion of successful background check and position specific pre-employment screening.By confirming below, I certify that I have read and agree with these statements.

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Submitted on December 08, 2015 at 03:56 AM by Kathleen Wilkie



Kathleen Patricia Wilkie, PhD

CONTACTINFORMATION

Department of Mathematics [email protected] University [email protected] Huntington Ave, Boston, MA, 02115 www.math.uwaterloo.ca/˜kpwilkie781-874-0728

INTERESTS • mathematical medicine• cancer systems biology• theoretical cancer immunology• cellular and tissue biomechanics

EDUCATION University of Waterloo, September 2005 – August 2010Waterloo, ON, CAN

Ph.D. in Applied Mathematics, conferred October 2010

Thesis Topic: Mathematical models of hydrocephalusAdvisor: Prof. Sivabal SivaloganathanResearch Area: Poroelastic and viscoelastic models of the brain

University of Waterloo, September 2003 – August 2005Waterloo, ON, CAN

M.Math. in Applied Mathematics, conferred October 2005

Thesis Topic: Localized medical image registrationAdvisor: Prof. Edward VrscayResearch Area: Mathematical imaging science and information theory

Memorial University of Newfoundland, July 2003 – August 2003St. John’s, NL, CAN

Atlantic Association for Research in the Mathematical Sciences summer school

University of Waterloo, September 1998 – April 2003Waterloo, ON, CAN

B.Math. with Distinction, conferred June 2003

Major: Applied MathematicsElectives: Electrical Engineering specializing in Control TheoryDetails: Dean’s Honour List and co-operative education program

RELATEDEXPERIENCE

Part-Time Lecturer September 2015 - May 2016Department of MathematicsNortheastern University, Boston, MA, USAI am currently teaching two sections of a multi-section course, Math 2321 - Calculus 3 forScience and Engineering to 70 students. In the spring term, I will teach an additional sectionof Math 2321 along with a section of Math 1342 - Calculus 2 for Science and Engineering.

Visiting Researcher December 2014 – February 2015Soto and Sonnenschein LaboratoryTufts University School of Medicine, Boston, MA, USADuring my short time in this Lab, I worked on developing a computational agent-basedmodel to explore the role of extracellular matrix composition in the development of acini orductal structures formed by breast epithelial cells, and the possible links with breast cancer.

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Assistant Investigator January 2014 – October 2014Research Associate January 2011 – December 2013Center of Cancer Systems BiologyResearch Instructor, Tufts University School of Medicine, Boston, MA, USAIn my postdoctoral work, I developed a systems biology approach to study cancer. My re-search focus is the systemic nature of the disease including stem cells, the immune response,inflammation, and cachexia. Mathematical tools used in this research include differentialequations, nonlinear dynamics, network theory, information theory, and statistical analysis.

Sessional Lecturer September 2010 – December 2010Department of Applied Mathematics January 2009 – April 2009University of Waterloo, Waterloo, ON, CAN January 2008 – April 2008In Fall 2010, I taught a single section course, MATH 228 - Differential Equations for the Sci-ences to 60 students, and one section of a multi-section course, MATH 237 - Calculus Threefor Honours Math to 110 students. In Winter 2009, I taught a single section course, MATH127 - Calculus One for the Sciences, to 200 students. In Winter 2008, I taught one section of amulti-section course, MATH 138 - Calculus Two for Honours Math, to 90 students.

Teaching Assistant September 2003 – April 2010Department of Applied MathematicsUniversity of Waterloo, Waterloo, ON, CANDuties included running tutorials, marking assignments, proctoring and marking tests andexams, organizing undergraduate markers, and one-on-one tutoring. Courses include:• MATH 115 - Linear Algebra for Engineering• MATH 117 - Calculus 1 for Engineering• MATH 119 - Calculus 2 for Engineering• MATH 137 - Calculus 1 for Honours Mathematics• MATH 138 - Calculus 2 for Honours Mathematics• MATH 211 - Advanced Calculus 1 for Electrical and Computer Engineers• MATH 237 - Calculus 3 for Honours Mathematics• AMATH 250 - Introduction to Differential Equations

Research Assistant May 2002 – August 2002Department of Applied MathematicsUniversity of Waterloo, Waterloo, ON, CANFunded partially by an NSERC USRA, I worked with Professor K.G. Lamb to modify a nu-merical model of internal gravity waves and to develop analytic solutions to validate thenumerical simulations.

Research Assistant September 2001 – December 2001Department of Applied MathematicsUniversity of Waterloo, Waterloo, ON, CANFunded partially by an NSERC USRA, I worked with Professor E.R. Vrscay on methods ofimage fusion using wavelet and fractal-wavelet techniques.

Research Assistant January 2001 – April 2001Climate Research GroupEnvironment Canada, Toronto, ON, CANI validated a regional climate model against physical data, investigated model weaknesses,and researched new models for cloud formation.

Editorial Assistant January 1999 – April 1999First Folio Resource Group Inc., Toronto, ON, CANI tested mathematics teaching software for quality assurance and wrote questions and solu-tions for a grade nine mathematics textbook.

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AWARDS Landahl Travel Grant July 2012National Award July 20112 × $500 award, granted on research merit to attend the Annual SMB meeting

SIAM Early Career Travel Award July 2012National Award$650 award plus registration, granted on research merit to attend the Workshop CelebratingDiversity at the SIAM Annual Meeting

NSF Travel Grant July 2011National Award$1000 award, granted on research merit to attend the Annual SMB meeting

Ontario Graduate Scholarship in Science and Technology January 2009 – April 2009Provincial Award$5000 award, granted on research merit and demonstration of leadership

Natural Sciences and Engineering September 2005 – August 2008Research Council of CanadaPostgraduate Scholarship DoctoralNational Award$63,000 over three years, granted on research and academic merit

President’s Graduate Scholarship September 2005 – August 2008Institutional Award$30,000 over three years, granted on research and academic merit

Natural Sciences and Engineering Research Council of Canada May 2004 – April 2005Postgraduate Scholarship MastersNational Award$17,300 award, granted on research and academic merit

Mathematics Provost Scholarship September 2003 – April 2004Institutional Award$3000 award, granted on research and academic merit

Rene Descartes Scholarship September 1998 – April 2003Institutional Award$5000 award, granted on academic merit

Natural Sciences and Engineering May 2002 – August 2002Research Council of Canada September 2001 – December 2001Undergraduate Student Research AwardNational Award2 × $4000 award, granted on research and academic merit

Arthur Beaumont Memorial Scholarship September 2001 – August 2002Institutional Award$1000 award, granted on academic merit

R.A. Wentzell Memorial Award September 2000 – August 2001Institutional Award$500 award, granted on academic merit

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UPCOMINGARTICLES

K.P. Wilkie and P. Hahnfeldt, Modeling the Dichotomy of the Immune Response to Cancer: Cyto-toxic Effects and Tumor-Promoting Inflammation, arXiv:1305.3634 [q-bio.CB], submitted to Bull.Math. Biol. April, 2015.

PUBLISHEDARTICLES

[Book Chapter] I. Kareva, K.P. Wilkie, and P. Hahnfeldt, The Power of the Tumor Microenvi-ronment: A Systemic Approach for a Systemic Disease, in Mathematical Oncology 2013 [Eds. A.d’Onofrio and A. Gandolfi], Springer New York, doi: 10.1007/978-1-4939-0458-7 6, 181–196,2014.

N. Almog, C. Briggs, A. Beheshti, L. Ma, K.P. Wilkie, R. Rietman, and L. Hlatky, Transcrip-tional Changes Induced by the Tumor Dormancy-Associated MicroRNA-190, Transcription, 4:4,177–191, 2013.

K.P. Wilkie and P. Hahnfeldt, Mathematical Models of Immune-Induced Cancer Dormancy andthe Emergence of Immune Evasion, Interface Focus, 3:4, 20130010, doi:10.1098/rsfs.2013.0010,2013.

K.P. Wilkie and P. Hahnfeldt, Tumor-Immune Dynamics Regulated in the Microenvironment In-form the Transient Nature of Immune-Induced Tumor Dormancy, Cancer Res. 73:12, 3534–3544,2013.

[Book Chapter] K.P. Wilkie, A Review of Mathematical Models of Cancer-Immune Interactions inthe Context of Tumor Dormancy, in Systems Biology of Tumor Dormancy [Eds. H. Enderling, N.Almog, and L. Hlatky] and Adv. Exp. Med. Biol. 734, 201-34, doi: 10.1007/978-1-4614-1445-2 10, 2013.

K.P. Wilkie, G. Nagra, and M. Johnston, A Mathematical Analysis of Physiological and Molecu-lar Mechanisms that Modulate Pressure Gradients and Facilitate Ventricular Expansion in Hydro-cephalus, Int. J. Num. Anal. Mod. B, 3:1, 65–81, 2012.

K.P. Wilkie, C.S. Drapaca, and S. Sivaloganathan, A Mathematical Investigation of the Role ofIntracranial Pressure Pulsations and Small Gradients in the Pathogenesis of Hydrocephalus, Int. J.Num. Anal. Mod. B, 3:1, 36–51, 2012.

K.P. Wilkie, C.S. Drapaca, and S. Sivaloganathan, Aging Impact on Brain Biomechanics withApplications to Hydrocephalus, Math. Med. Biol. 29:2, 145–161, 2012.

K.P. Wilkie, C.S. Drapaca, and S. Sivaloganathan, A Nonlinear Viscoelastic Fractional Deriva-tive Model of Infant Hydrocephalus, App. Math. Comput. 217:21, 8693–8704, 2011.

C. Boucher and K. Wilkie, Why Large CLOSEST STRING Instances Are Easy to Solve in Practice,String Processing and Information Retrieval, LNCS, 6393, 106–117, 2010.

K.P. Wilkie, C.S. Drapaca, and S. Sivaloganathan, A Theoretical Study of the Effect of Intraven-tricular Pulsations on the Pathogenesis of Hydrocephalus, App. Math. Comput. 215:9, 3181–3191,2010.

K.P. Wilkie and E.R. Vrscay, Mutual Information-Based Methods to Improve Local Region-of-Interest Image Registration, Image Analysis and Recognition, LNCS, 3656, 63-72, 2005.

K.G. Lamb and K.P. Wilkie, Conjugate Flows for Waves with Trapped Cores, Phys. Fluids, 16:12,4685–4695, 2004.

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WORKSHOPREPORTS

Ronald Begg and Kathleen Wilkie, A Mechanism for Ventricular Expansion in Communicat-ing Hydrocephalus, Proceedings of the OCCAM-Fields-MITACS Biomedical Problems Solv-ing Workshop, http://www.fields.utoronto.ca/programs/scientific/08-09/biomedical/Proc_2009_OFM_Biomed_PSW.pdf, Toronto, June 22–26, 2009.

CONFERENCEAND WORKSHOPPRESENTATIONSWITH ABSTRACT

K.P. Wilkie, R. Batra, L. Ma, C. Briggs, P. Hahnfeldt, and L. Hlatky, The Role of Tumor-DerivedSoluble Factors and Microvesicles in Tumor-Host Interactions and Cancer Cachexia, ICBP-PSOCMath Modeling Meeting, Tampa, FL, February 26-28, 2015 (Invited Speaker).

K.P. Wilkie, Modeling in Cancer Immunology, Association for the Advancement of ScienceAAAS Annual Meeting, Boston, MA, February 14-18, 2013 (Invited Minisymposium Speaker).

K.P. Wilkie and P. Hahnfeldt, Immune Modulation of Tumor Growth Through Inflammation andPredation, Annual Meeting of the Society for Mathematical Biology, NiMBioS and the Uni-versity of Tennessee, Knoxville, July 25-28, 2012.Organizer of minisymposium on Cancer Immunology.

K.P. Wilkie and P. Hahnfeldt, Immunotherapy and Aging Effects in Immune Modulated TumorGrowth, Annual Meeting of the Society for Industrial and Applied Mathematics, Minneapo-lis, July 9-13, 2012 (Invited Minisymposium Speaker).

K.P. Wilkie and P. Hahnfeldt, A Mathematical Model of Immune-Induced Tumor Dormancy andthe Emergence of Immune Evasion, Canadian Applied and Industrial Mathematics AnnualMeeting, Fields Institute, Toronto, June 24-28, 2012 (Invited Speaker).

Kathleen Wilkie and Philip Hahnfeldt, A Mathematical Model of Immune Modulation of Tu-mor Growth, Workshop on Mathematical Oncology IV: Integrative Cancer Biology, Centre forMathematical Medicine, Fields Institute, Toronto, March 29-31, 2012 (Invited Speaker).

Kathleen Wilkie, Mathematical Models of Tumor-Immune Interactions and Immune-Induced Tu-mor Growth Modulation, Workshop on Systems Biology of Tumor Dormancy, Center of CancerSystems Biology, Boston, July 25–28, 2011 (Invited Speaker).

Kathleen Wilkie, The Effects of Aging on Brain Biomechanics and an Examination of the Pulsation-Damage Hypothesis for Hydrocephalus, Brain Neuromechanics Workshop, Centre for Mathe-matical Medicine, Fields Institute, Toronto, July 26–28, 2010 (Invited Speaker).

K.P. Wilkie, C.S. Drapaca, and S. Sivaloganathan, A Nonlinear Viscoelastic Fractional Deriva-tive Model of Infant Hydrocephalus, 16th US National Congress of Theoretical and AppliedMechanics, Penn State, June 27 – July 2, 2010 (Extended Abstract).

Kathleen Wilkie, Examining Cerebrospinal Fluid Pulsations as a Causative Mechanism for Hydro-cephalus, Annual Meeting of the Society for Mathematical Biology, Toronto, July 30 – August2, 2008.

K.P. Wilkie A Pulsatile Cerebrospinal Fluid Model for Hydrocephalus, Workshop on Brain Biome-chanics: Mathematical Modelling of Hydrocephalus and Syringomyelia, Centre for Mathe-matical Medicine, Fields Institute, Toronto, July 27, 2007.

CONFERENCEAND WORKSHOPPOSTERS

K.P. Wilkie and P. Hahnfeldt, Modelling Immunomodulation of Tumor Growth, ECMTB andAnnual Meeting of the Society for Mathematical Biology, Krakow, July 28–Aug 2, 2011.

Kathleen P. Wilkie and Dr. Edward R. Vrscay, Mutual Information Based Methods to LocalizeImage Registration, Workshop on Modelling in Oncology: Problems and Challenges, Centrefor Mathematical Medicine, Fields Institute, Toronto, October 5, 2005.winner of best poster prize.

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http://www.fields.utoronto.ca/programs/scientific/08-09/biomedical/Proc_2009_OFM_Biomed_PSW.pdf

http://www.fields.utoronto.ca/programs/scientific/08-09/biomedical/Proc_2009_OFM_Biomed_PSW.pdf

PHDTHESIS

Kathleen P. Wilkie, Cerebrospinal Fluid Pulsations and Aging Effects in Mathematical Models ofHydrocephalus, University of Waterloo, ON, CAN, 2010.

MASTERSTHESIS

Kathleen P. Wilkie, Mutual Information Based Methods to Localize Image Registration, Univer-sity of Waterloo, Waterloo, ON, CAN, 2005.

PROFESSIONALSERVICE

Association of Early Career Cancer Systems Biologists Member Sept. 2015 - PresentCancer Systems Biology Steering Committee Member Sept. 2014 – Aug. 2015A founding member of the new Association of Early Career Cancer Systems Biologists.Member of the Community subcommittee tasked with connecting the community (espe-cially early stage investigators) through social media and organized events.

Steering Committee Meeting Co-Chair Jan. 2014 – Sept. 2014Early Stage Investigators in Cancer Systems Biology - ICBPCo-organizer of the Early Stage Investigators in Cancer Systems Biology Meeting for theNCI’s Integrative Cancer Biology Program, Sept. 4–5 2014, Cambridge, Massachusetts.

ICBP Undergraduate Research Fellow Mentor June 2014 – Aug. 2014Mentor for an undergraduate cancer research fellow/intern through the Education and Out-reach Program of the NCI’s Integrative Cancer Biology Program.

ICBP Jr Investigators Meetings Jan. 2012 – Nov. 2013Co-organizer of two Junior Investigators Meetings for the NCI’s Integrative Cancer BiologyProgram.• Co-Chair: Nov. 13–15 2013 meeting in Bethesda, Maryland Jan. 2013 – Nov. 2013• Co-Organizer: Sept. 26–28 2012 meeting in Seattle, Washington Jan. 2012 – Nov. 2012

Applied Mathematics Graduate Student Representative (UW) May 2009 – May 2010• Math Faculty Graduate Studies Committee (non-voting member)• Applied Math Departmental Graduate Affairs Committee (non-voting member)

Graduate Student Association (GSA) Departmental Councillor Oct. 2005 – Aug. 2009• GSA Long Range Planning Committee May 2008 – Apr. 2009• GSA Activities Committee Oct. 2005 – Apr. 2008

Graduate Student Senator (to UW Senate) May 2007 – Apr. 2009• Senate Long Range Planning Committee

Mathematics Faculty Graduate Student Representative (UW) May 2006 – Apr. 2008• Math Faculty Representative Council May 2007 – Apr. 2008• Math Faculty Council• Math Faculty Graduate Studies Committee

Other Leadership and Community Outreach• Mentor at the SMB Annual Meeting July 2012• UW Math Faculty graduate student orientation Sept. 2007 – Sept. 2010• UW Applied Math graduate student orientation Sept. 2007 – Sept. 2009• UW Women In Mathematics high school outreach Mar. 2005 – May 2010• UW Math Faculty Phone-a-thon Apr. 2005 – Apr. 2007• UW Campus Day Mar. 2004

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References for Kathleen Wilkie, PhD

1. Philip Hahnfeldt, PhD [Postdoctoral Advisor]Senior Investigator, Center of Cancer Systems Biology,Boston, MA, 02135 USAemail: [email protected]

2. Lynn Hlatky, PhD [Director of CCSB]Director, Center of Cancer Systems Biology,Boston, MA, 02135 USAemail: [email protected]

3. Sivabal Sivaloganathan, PhD [PhD Supervisor]Professor, Department of Applied Mathematics, University of WaterlooDirector, Center for Mathematical Medicine, Fields InstituteWaterloo, ON, N2L 3G1 CANemail: [email protected]

4. David McKinnon, PhD [Teaching]Professor, Department of Pure Mathematics, University of WaterlooWaterloo, ON, N2L 3G1 CANemail: [email protected]

5. Dan Wolczuk [Teaching]Lecturer, Faculty of Mathematics, University of WaterlooWaterloo, ON, N2L 3G1 CANemail: [email protected]

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Department of MathematicsNortheastern University567 Lake Hall360 Huntington AveBoston MA 02115 USA

December 7, 2015

Dr. Richard M. SingleDepartment of Mathematics and StatisticsUniversity of VermontBurlington, VT, 05405

To the Search Committee:

I am writing to apply for the tenure-track Assistant Professor position at the Universityof Vermont. As a biomedical mathematician, an applied mathematician inspired bythe interface of mathematics with biology and medicine, I combine various conceptsfrom mathematics and statistics to study the systems biology of Cancer. Currently,I am a Lecturer at Northeastern University, Boston, MA. Prior to this, I was anassistant investigator in the integrative Center of Cancer Systems Biology at TuftsUniversity School of Medicine, Boston, MA, and my undergraduate and graduatedegrees are from the Faculty of Mathematics at the University of Waterloo, ON.

In my research, I use a systems biology approach that attempts to integrate datafrom multiple biological scales into predictive mathematical frameworks. Becausebiology is complex (and messy), I strive to develop mathematical models that elucidatebiological mechanisms without confounding the problem with mathematical complexity.My doctoral dissertation explored the validity of several medical hypotheses forthe development of hydrocephalus using continuum models based on poroelastic orviscoelastic materials (with fractional derivatives). My current work uses mathematicalmodels to deconvolve the complex interactions involved in the systemic response of apatient to cancer. I developed a mathematical framework, representing a paradigmshift in theoretical cancer immunology, away from predator-prey models towardsan allowance for both stimulatory and inhibitory actions, which better predicts thenonlinear dynamics of tumor growth observed clinically. In cancer cachexia, the diseasecauses irreversible muscle and adipose tissue loss, which severely degrades health. Myresearch attempts to integrate data and conclusions from several biological scales(gene expression, protein interactions, cellular function, and the physical diffusion ofsignaling proteins) into a predictive (population-based) model for the general healthof the whole patient. Techniques from computational biology, differential equations,nonlinear dynamics, statistics, and graph / network theory are used.


I recently returned to the classroom after a 4 year research-only postdoctoral position,and I am quite enjoying the rewards of working closely with students again. In total,I have taught six undergraduate courses in calculus and differential equations, and Iwill teach two more in the Spring term at Northeastern. When lecturing, I work hardto motivate topics and to present ideas clearly, including visual aids to demonstrateconcepts, and real-world examples to motivate theory. I am eager to develop andteach courses related to my research, and to mathematical biology in general. In 2014,I mentored an undergraduate student at the Center of Cancer Systems Biology, and Ilook forward to advising more students on their own research projects.

Through an initiative started by the National Cancer Institute, I have been involvedfor the past several years in the formation of a community of early stage investigatorsin Cancer Systems Biology. We started with small meetings and are now growingto organize a full conference starting in 2016. I also co-run a social media page toconnect researchers, communicate information, and discuss challenges in our new fieldof research (www.facebook.com/CancerSysBio/).

I enjoy the interdisciplinary nature of my work, and have previous or current collabo-rations with research hospitals in both Toronto and Boston. Given the opportunity, Iwould seek out new collaborations within the Mathematics and Statistics Department,the School of Engineering, the College of Medicine, and the Vermont Cancer Center.

In general, I am looking for an environment where I can continue to teach and workclosely with students, while maintaining an active research profile. I feel that theUniversity of Vermont may be a place where I can grow both as an educator and as aresearcher.

I am enclosing my CV, research statement, teaching dossier, and a list of references.Thank you for your consideration.

Sincerely,

Kathleen Wilkie


www.facebook.com/CancerSysBio/

Research StatementKathleen Wilkie

Mathematics is the heart of Systems Biology. New biological problems demand new mathe-matical techniques. Through mathematics, we integrate diverse data types into predictivehypothesis-testing models, and interpret results to advance biological understanding.

I explore the interface of applied mathematics with biology and medicine. My mathematicalexperience with ordinary and partial differential equations, continuum and fluid mechanics,nonlinear population dynamics, numerical methods, and signal and image processing com-plement my collaborative experience with clinicians, pathologists, and biologists at researchhospitals and in the Center of Cancer Systems Biology. Together they give me the intuitionto identify and analyze interesting biological questions that create advances in modelingapproaches, numerical methods, analysis or data visualization techniques, and biologicalunderstanding. My approach involves modeling medical hypotheses with mathematicalformulations, analyzing the models, and interpreting results to make meaningful biologicalconclusions. The last step allows us to provide positive feedback to collaborating medicalclinicians or biologists. The investigation leads to new mathematics, but the feedback formsa cycle of collaboration driving further investigation and extends our understanding ofunderlying biology.

My research is motivated by my continued study of the systemic nature of cancer. Thedisease affects the entire host on multiple biological scales, and thus, requires a systemsbiology approach to integrate both experimental data and modeling conclusions from onescale to the next.

Multi-Scale Modeling of Cancer Cachexia

Multi-scale phenomena pose a unique mathematical challenge because each scale must beconsidered at it’s own characteristic length and time. Often, approximations or simplifyingassumptions made at one scale are not valid at the next. Thus, integrating the scales into oneunifying framework poses many challenges.

Cancer is inherently multi-scale. Even when locally constrained, it affects the entire host ona systemic level. For example, blood can carry tumour-derived intercellular communicationfactors through the body, disturbing homeostasis, triggering inflammation, and potentiallyinitiating muscle and adipose tissue loss leading to cancer cachexia. My current researchuses diverse mathematical techniques to integrate the myriad changes induced by cancer-hostsignaling into a predictive host-level dynamical system. Altered signaling cascades areidentified from statistical and bioinformatics algorithms and conclusions are lifted from onescale to the next in the biological (and thus mathematical) hierarchy by careful constructionof the next mathematical formulation.

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Kathleen P. Wilkie Research Statement 2 of 4

How to effectively integrate data from multiple scales to develop predictive mathematical orcomputational tools and to draw meaningful conclusions related to cancer biology or, morepressing, to cancer treatment, is an extremely important and extremely complex problem.The explosion of readily available genetic data has lead to an overwhelming collection ofdata that is difficult to interpret and draw conclusions from. While many researchers aredeveloping methods to analyze this data, my research aims to develop methods to integratethe data from one scale to the next, lifting genetic and mutational data through the biologicalhierarchy, to more readily-observable macroscopic scales.

Towards this goal, my main research project integrates three biological scales: genetic, tissue,and organism. First, genetic-level changes are analyzed using statistics and bioinformaticsto infer alterations to biological pathways and thus cell function. Next, intercellular com-munication is modeled by the diffusion partial differential equation where tumour-derivedsignaling proteins and microvessicles (larger packages of proteins with different diffusiveproperties) move out of the blood stream into host tissues. Finally, incorporating conclu-sions drawn from the previous two scales, an organism-level population-based ordinarydifferential equation model predicts the interactions of tumour, muscle, and adipose tissuesin the development of cancer cachexia. The nonlinear dynamics involved in the developmentof this disease are amenable to mathematical modeling, and with no treatment option forcachexia at this time, the use of mathematical modeling for hypothesis testing is a fiscallyresponsible companion to laboratory experimentation.

Population Dynamics for Cancer-Immune Interactions

A significant factor in the systemic nature of cancer is the immune response. Cancer-immune interactions are typically described by preditor-prey models, but in fact, immunecells can both inhibit and promote the disease. Thus, the classic preditor-prey model mustbe expanded to account for stimulatory actions and to better describe the resulting nonlineardynamics, including those of tumor dormancy where growth is temporarily forestalled.

The extreme successes and failures of cancer immunotherapy, for example, derive from anincomplete understanding of cancer-immune dynamics, since individual patient responsescannot yet be predicted. In my postdoctoral work, a collaboration with Philip Hahnfeldt[CCSB], I built a mathematical framework to better anticipate tumour-immune evolutionand its treatment response. Typical models in this area ignore all tumour-promoting effectsof the immune response and consider only predatory actions. Current biological research,however, has shown that immune mechanisms can stimulate tumour initiation, enhanceprogression, and aid metastasis. To explore the competing roles of the systemic immuneresponse, I constructed a system of ordinary differential equations that incorporate bothstimulatory and inhibitory actions of an immune response to cancer. Thus, this model isbetter positioned over existing models to predict the nonlinear dynamics of tumour growthand treatment response, including immunotherapies and anti-angiogenics.



This framework is presented fully in a manuscript submitted to The Bulletin of MathematicalBiology and briefly discussed in chapter 6 of Mathematical Oncology 2013. In this work, Idescribe how the use of a generalized logistic growth equation captures inherent variability(through model non-identifiability) often neglected in tumour growth, and how this variabilityhas the potential to significantly alter tumour growth dynamics and thus treatment successrates. I also formalize the polarity of the inflammatory tumour micro-environment anddemonstrate that to improve tumour control a pro-tumour state must be converted into ananti-tumour state through immunotherapy. The polarized inflammatory states, determiningthe amount of immune-stimulation, are controlled by intercellular signaling (the cytokinemilieu), and thus directly impact tumour fate.

A model derived from the above formulation, published in Cancer Research, investigates theimmune-induced dormant cancer state and the challenges of maintaining this chronic state.Mathematically, the dormant state is obtained by controlling a tumour growth trajectorywithin proximity to the separatrix of a bistable dynamical system. This contradicts theprevailing view in the literature where dormancy is described by a stable attractor with it’sown basin of attraction. Biological implications of my inherently unstable opposing viewimprove understanding of the transient nature of immune-induced tumour dormancy.

In dormancy, however, cancer cells can evolve immune-resistance mechanisms leading toescape. My manuscript published in Interface Focus, uses a data-driven approach to explorethe resulting dynamics of tumour escape from the dormant state through the emergenceof hypothesized immune-resistance mechanisms (decreased immune predation efficacy ordecreased immune recruitment potential - represented by different model parameters toallow testing). Minimizing recurrence through long-term maintenance of the dormant statewill require a complete understanding of escape mechanisms, and mathematical modelingcan help obtain this goal, leading to improved treatment design and cancer as a chronicdisease.

Protein Interaction Network Analysis

In an ongoing collaborative project with Michael La Croix (MIT) and the Center of CancerSystems Biology, I am investigating a possible metric to measure the relationship betweenthe protein-protein interaction network structure of a specific cancer type and the treat-abilityor survivability of that type. Using concepts from graph theory and information theory, weare trying to link protein-level changes and network complexity to disease survivability.Currently more data is being sought to test our hypothesized metric which compares theentropy of the graph constructed from the cancer network to that of a random graph with thesame number of vertices and edges.



Agent Models, Hybrid Models, and Living Tissue Biomechanics

In collaboration with the Soto and Sonnenschein Lab at Tufts University School of Medicine,I am developing a computational (agent-based) model to examine the role of extracellularmatrix composition in ductal pattern formation and cancer. I plan to extend this investiga-tion, by developing a macroscopic continuum description of living tissue that incorporatestemporal changes in cell behaviour. Particularly, incorporating intercellular communicationthrough mechanical signaling: cells can sense and internalize changes in tissue stiffnesswhich can induce changes in gene expression and cell behaviour, resulting in cell-inducedchanges in tissue stiffness, and thus creating a feedback loop. This feedback mechanismmay be responsible for the synchronization of cellular behaviour over large regions (self-organizing behaviours), and may be observed through the construction of a hybrid modelwhere the agents lie above, and interact with, the continuum description below.

In this endeavor, I would revisit aspects of my doctoral thesis wherein I developed fractional-derivative based viscoelastic models for brain tissue (published in App Math Comput [2010],Math Med Biol, and Int J Num Anal Mod B [2012]). The fractional derivative introducesa history dependence with fading memory. A possible application is cancer invasion intosurrounding tissue since tissue stiffening is observed around many tumours and is hypothe-sized to lead to more aggressive tumours. A mathematical model describing the invasionprocesses would help identify significant factors in the feedback process driving tumourevolution and to assess possible mechanically-targeted therapies.

Career Goals

I plan to establish an externally funded research program that is highly collaborative andinclusive of student researchers. Short-term projects derived from my current or pastwork include deriving equations for cancer stem cell growth with both environmental andpopulation regulation; constructing a model to investigate the effects of age on the immuneresponse and cancer risk (known to be non-monotonic with age); and investigating thevariability of in silico patient cohorts, parameter ensembles generated by Markov ChainMonte Carlo methods, to disease archetypes and evolutionary paths, and linking thesearchetypes to genetic signatures.

Long term projects, in general, involve the formalization of methods to integrate multi-scale and diverse data or modeling results into predictive mathematical frameworks, withparticular focus on short and long range intercellular communication through diffusiblefactors and mechanical sensing. To accomplish this, ideas from nonlinear and populationdynamics, ecology, continuum mechanics, bioinformatics, and other areas, will be combinedinto multi-scale continuous, discrete, or hybrid mathematical models. This work willprovide insights into the mechanisms of population-level emerging behaviours similar tothose observed in living tissues, fish swarms, or herd pattern formations.


Teaching StatementKathleen Wilkie

My goal when teaching mathematics is to show students how to think and reason aboutproblems with creativity, confidence, and intuition.

When I lecture, I present ideas in a clear manner that flows naturally and logically from ourexisting knowledge. If possible, I use multiple explanations, such as algebraic, geometric,or visual, to demonstrate the same concept. In this way, I hope to connect to studentswith different learning styles, and to remove the sense of mystery or “magic” that somestudents believe exists in mathematics. I try to explain, not only the technical steps involvedin problems, but also the steps involved in the thought process and possible indicationsthat a mistake has been made. Encouraging students to think about mathematics and tounderstand its development, instead of memorizing machinery, helps them to develop asense of intuition that leads to success.

I aim to increase the comfort and confidence of students with regards to their mathematicalabilities. Discussing technical strategies and demonstrating how to check their work helpsto achieve this goal. Developing an ease-of-use of mathematics allows students to integratetheir knowledge into everyday circumstances, whether it be in filing taxes or criticallythinking about the latest medical finding on the risks associated with eating bacon. Perhapsone of my best student compliments, overheard in the hallway by a colleague, was that astudent preferred my section of calculus to another because I “made them feel smart”.

I believe that one of the main challenges of teaching mathematics is that many students donot know what the subject is really about, and thus they believe it to be boring and of no useto them. To address this, I try to project enthusiasm and interest in my lectures and strive torelate topics to everyday examples, such as velocity being the derivative of distance withrespect to time, or our body acting as a feedback controller to adjust the temperature in theshower. To counter the theoretical nature of mathematics, I try to incorporate visual aidsinto lectures to demonstrate concepts whenever possible. Examples of this include a deckof cards to demonstrate the divergence of the harmonic series, sound clips to demonstratethe phenomenon of beats in forced oscillators, and video clips to demonstrate the peculiarbehavior of non-newtonian fluids. In addition, I find that relating the techniques learned inthe course to real-world applications, new technologies, and current research topics, helps todemonstrate usefulness and to pique interest. For example, jpeg compression of images is agreat application of Fourier Transforms.

For student evaluation through assignments or exams, I like to include a challenge questionin addition to the standard array of questions. The challenge question requires creative andintuitive thought processes and is useful in distinguishing excellent students from goodstudents as well as promoting student interest. An example question may be to calculate the

1


Kathleen P. Wilkie Teaching Statement 2 of 2

drug concentration in a patient given their mass, drug dosage, and clearance rate. My hopeis that these questions spark interest in the students and encourage them to read and thinkabout the course topics on their own.

I strive to establish an open classroom so that everyone feels comfortable asking andanswering questions. When students are interacting in lectures, I can more easily assess theirprogress and adjust my lectures accordingly. Feedback from end-of-term student courseevaluations indicates that students generally find me to be open and fair and my lectures tobe of good quality.

As a female mathematician, I believe it is important to be a visible role model and act as amentor for young women in my field, to support and encourage the growth of diversity inmathematics. One of the primary ways to accomplish this task is to teach courses. Asidefrom lecturing, I have participated in several Women in Mathematics outreach events aimedat promoting mathematics as a career choice for female high school students.

To date, I have taught the following courses at Northeastern University (NEU) and theUniversity of Waterloo (UW):

• Math 2321 - Calculus 3 for Science and Engineering (NEU)

• Math 127 - Calculus I for the Sciences (UW),

• Math 138 - Calculus II for Honours Mathematics (UW),

• Math 237 - Calculus III for Honours Mathematics (UW), and

• Math 228 - Differential Equations for Physics and Chemistry (UW).

Three of these courses were co-ordinated courses (Math 2321, Math 138, and Math 237) andtwo were single section courses where I was fully responsible for all course content (Math127 and Math 228). Samples of the course material that I prepared for these single-sectioncourses aimed at science majors, and summaries of my course evaluations, can be found inmy Teaching Portfolio.


Kathleen P. Wilkie 1 of 9

Teaching Portfolio

A sample research presentation with slides and audio can be found at

http://www.fields.utoronto.ca/audio/11-12/mathoncology/wilkie/.

This talk was given at the Fields Institute, Toronto, Canada, on March 31, 2012 as a part ofthe Workshop on Mathematical Oncology IV: Integrative Cancer Biology.

I have included some assignments and handouts from the two single-section courses (non-coordinated) that I taught at the University of Waterloo, Canada. Assignments typicallyhad the format of several standard questions to pratice the learned technique followed by achallenge question to apply the technique and hopefully motivate the material and stimulateinterest in the students.

Figure 1 is Assignment 1 from my Math 127 - Calculus 1 for the Sciences course.

Figure 2 is Assignment 6 from my Math 127 - Calculus 1 for the Sciences course.

Figure 3 is Assignment 1 from my Math 228 - Differential Equations for Physics andChemistry course.

Figure 4 is an exam preparation handout from my Math 228 - Differential Equations forPhysics and Chemistry course.

I also include teaching evaluation summaries from the last two courses I taught (in Fall2010) and some sample student comments.

Figure 5 is the teaching evaluation summary for my Math 228 - Differential Equations forPhysics and Chemistry course.

Figure 6 contains student evaluation comments for Math 228 - Differential Equations forPhysics and Chemistry.

Figure 7 is the teaching evaluation summary and a sample of student comments for myMath 237 - Calculus 3 for Honours Mathematics course.

Figure 8 contains more student evaluation comments for Math 237 - Calculus 3 for Hon-ours Mathematics.


http://www.fields.utoronto.ca/audio/11-12/mathoncology/wilkie/

Kathleen

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Figure 1: Assignment 1 for my Math 127 - Calculus 1 for the Sciences course at the University of Waterloo, Canada.

Math 127 ASSIGNMENT 1 Winter 2009

Submit all problems by 9 am on Wednesday, January 14th in the drop box for your tutorial section.Assignments put into the wrong drop slot will not be marked. All solutions must be clearly stated andfully justified. You should be able to do all sketches by hand, without using a calculator.

1. Solve the inequalities to find the corresponding intervals for x and illustrate each solutionon a number line.

(a) −4 ≤ x − 2 < 3 (b) 1 + 6x > 4 − 3x (c) x2 + 2x < −1 (d) x3 ≤ x

2. Solve the absolute value relations for x and illustrate the solutions on a number line.

(a) |5x − 2| < 6 (b)∣∣∣∣1x

∣∣∣∣ > 3 (c) |x − 1| = |x + 1|

3. (a) Graph the following lines on the same sketch.(i) y1 = 1

2 x + 1 (ii) y2 = 2x − 1(b) Give an interval of x which contains the intersection point of the 2 lines.(c) Find the point of intersection (i.e. where y1 = y2).

4. Find the equation and sketch each of the following:

(a) the line passing through the points (−1, 1) and (1, 0),(b) the line with slope 3 and y-intercept −2.

5. Sketch and name the following conics:

(a)x2

4+

y2

1= 4 (b)

x2

22 − y2

42 = 1 (c) y = x2 + 2x

6. (a) If a comet travels along the hyperbola given byx2

a2 − y2

b2 = 1 and a planet is located

at the focus of the hyperbola at (c, 0) where c2 = a2 + b2, find the closest distance thatthe comet ever comes to the planet. Only consider the positive x-axis branch of thehyperbola. Give a sketch to illustrate your answer.Hint: recall that for each point on the hyperbola P, the distance from P to the focus at(−c, 0) minus the distance from P to the focus at (c, 0) is always constant.

(b) If a = b = 1, find the smallest distance from the comet to the planet.

7. Kelly shovels her driveway for 10 minutes to get her bike out. She then bikes 20 minutesto the rock climbing gym where she climbs for 1 hour. She then bikes home a faster route,taking only 10 minutes. If she burns 5 calories/min shovelling, 10 calories/min biking and15 calories/min climbing, how many calories did she burn? Give a sketch of calories burnedas a function of time. Indicate the slope of each line segment on your sketch.

8. For the graph on the right answer the following:

(a) Find f (−3), f (2), g(−2), g(0), g(1).

(b) Estimate the points of intersection where f (x) = g(x).

(c) Give the intervals where f is increasing and decreasing.

(d) Give the domain of f and g.

(e) Give the range of f and g.

gf

-4 -3 -2 -1 0 1 2 3 4

-4

-3

-2

-1

1

2

3

4

9. Explain with a sketch how to test whether or not a given graph is a function. Give an exam-ple of a graph that passes the test and one that fails the test. What is the test checking thatthe graph satisfies?

10. Sketch a rough graph of the temperature outside today as a function of time. Be sure toindicate the date on your graph.

11. For each case, determine if f and g are even, odd, or neither:

(a)

f g

(b) f (x) = x2 − 1 and g(x) = x5 + x3.

(c) f (x) = x|x| and g(x) = |x|.

12. If y = 3x − 2 give the equation of a line that is parallel to y and the equation of a line that isperpendicular to y. Sketch all 3 lines on one graph.

CHALLENGE QUESTION 1

(a) The value of π is defined as the ratio of the circumference, C, to the diameter, d, of a circle:π = C

d = C2r , where r is the radius of the circle. So the circumference of a circle is then

C = 2πr. Following Leibniz’s love of chopping things up into smaller and smaller parts,cut the circle into 4 sections. Arrange the sections to approximate a rectangle. Now do thisagain using 8 sections. Imagine what the approximate rectangle would look like for 16 or 32sections. Using the formula for area of a rectangle (A = base x height), estimate the area ofthe approximate rectangle you made by rearranging the sections. As the number of sectionsused becomes infinite, this estimate becomes exact, and now you know why π occurs in theformula for the area of a circle.

(b) Thinking of yourself as a cylinder, estimate how much skin covers your body (i.e. yoursurface area) in m2. You can check your estimate at http://www.ultradrive.com/bsac.htm.

(c) Body surface area is used in medicine to calculate drug dosages. If a drug dose (in mg/day)is determined by d(x) = x3 − x2 + x, where x is the body surface area in m2, how much ofthe drug should you be given per day?

1Normally, assignments and exams will end with a challenging question, worth not more than 10% of the assignmentor exam mark. Be sure to complete all routine problems before spending too much time on this.


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Figure 2: Assignment 6 for my Math 127 - Calculus 1 for the Sciences course at the University of Waterloo, Canada.

Math 127 ASSIGNMENT 6 Winter 2009

Submit all problems by 9am on Wednesday, February 25th in the drop box associated with yourtutorial section and the first letter of your last name. Assignments put into the wrong drop slot willnot be marked. All solutions must be clearly stated and fully justified. You should be able to do allsketches by hand, without using a calculator.

1. Print your name, ID number, course number and tutorial section number clearly on the topof the front page (or second page) of your assignment. [Yes, seriously, do this now please.]

2. Differentiate the following functions:

(a) V(r) = 43πr3 (b) f (x) =

( 13 x

)4(c) y =

4x4 + 3x3 + 2x2 + x√x

(d) h(x) =(

x +1x

)2

(e) g(x) = 3√

x + 4√

x (f) y = 3t−58 + et+3

3. Find the derivative of the following:

(a) y = ex (x3 + 3x)

(b) f (t) =et

t3 (c) f (t) =t3

et

(d) g(x) =4x2 − 21 + 3x

(e) y =t3 + 3t2

t4 − 3t2 + 2(f) z(w) = w

32 (w + 2ew)

4. Differentiate by first writing the function in terms of sin, cos, or tan:

(a) f (x) = 4x3 + tan x (b) y = sin x + 12 cos x + 1

3 cot x (c) g(t) = t5 sec(t)

(d) f (t) =t

3 − tan t(e) f (θ) =

sec θ

sec θ + 1(f) y =

cos xx2

5. Find an equation for the tangent line to the given curve at the given point.

(a) y = 5√

x at (1, 1) (b) f (x) =ex

xat (1, e)

(c) g(x) = x + sin x at (0, 0) (d) y = cos(π2 cos x

)at (0, 0)

6. Differentiate the following functions.

(a) F(x) =(3x2 + 4x5 − 3

)6 (b) g(t) =3

(t3 + 3)3 (c) y = tan(1 + x2)

(d) f (z) = ze−z (e) y = sin(

1 − e−2x

1 + e2x

)

7. Find the first and second derivatives of the functions.

(a) y = 2x3 + 5x32 (b) y =

1cos(t2)

(c) y = eex

8. Use implicit differentiation to finddydx

for each expression.

(a) x3 + y4 = 27 (b) 3√

x + 3√

y = 1 (c) sin(x2y) = x2y2

(d) g(t) + t sin(

g(t))= t2 (e) 8x3 + y3 = 8 (f) Find y′′ for the curve in (e).

9. Find the equation to the tangent line for each curve at the given point.

(a) x2 + y2 = (2x2 + 2y2 − x)2 at (0, 12 ) (b) y = ln

(xex2

)at (1, 1)

10. For something a bit different, differentiate the following:

(a) y = arctan( 3√

x) (b) f (x) = arcsin(1 + 3x2) (c) g(x) = arccos(e5x)

(d) y = sin(ln x) (e) f (x) = ln (e−x + xe−x) (f) g(x) =√

xex 3√

x5 + 4xx2 + 3

(g) y =√

xx (h) y = xx sin x

CHALLENGE QUESTION 1

(a) Using the chain rule, findd

dx(log10 x

). Hint: start with the cancellation equation.

(b) The pH scale is used to compare the acidity of different solutions. It is defined as

pH = − log10 x

where x is the concentration of hydrogen ions contained in the solution. Find the rate ofchange of pH with respect to hydrogen ion concentration when pH is 7.4 (the pH level ofblood).

(c) Living cells that do not have enough oxygen in their environment metabolize by anaerobicrespiration. Cancer cells inside a tumour are an example of such cells. If a tumourous regioninitially has a pH level of 7.4 and the cells anaerobically respirate such that they cause thehydrogen ion concentration to increase by 10−8 per hour, find the rate of change of pH levelwith respect to time in the tumour.

(d) Assuming the change in pH in the tumour environment can be modelled by a linear functionof time with the form

pH(t) = 7.4 +ddt

(pH) t,

find the time when the tumour environment will have a pH of 6.6 (the pH of milk).

1Normally, assignments and exams will end with a challenging question, worth not more than 10% of the assignmentor exam mark. Be sure to complete all routine problems before spending too much time on this.


Kathleen P. Wilkie Teaching Portfolio 4 of 9

Figure 3: Assignment 1 for my Math 228 - Differential Equations for Physics and Chem-istry course at the University of Waterloo, Canada.

MATH 228 Assignment 1 Fall 2010DUE: In class, Wednesday September 29, 2010

Read chapters 2.1 – 2.3 and then answer the following questions.

1. Using the Existence - Uniqueness Theorem covered in class, determine if the DE y′ =√y2 − 9

has a unique solution through each of the given points.

(a) (1, 4) (b) (5, 3)

2. Find the equilibrium solutions and give a qualitative sketch of solutions for the given DEs.Include a phase line to help you sketch the solutions. Classify the equilibrium solutions. Youmight wish to check concavity to help sketch the curves.

(a)dy

dx= 10 + 3y − y2 (b)

dy

dx= y2(16− y2)

3. Solve the given differential equations using the Separation of Variables Method. Apply theinitial condition if given.

(a) xdy

dx= 4y (b)

dy

dx=

y2 − 1

x2 − 1, y(2) = 2

4. Solve the given linear first order differential equations using the Integrating Factor Method.Apply the initial condition if given.

(a) y′ + 2xy = x3 (b) (x+ 1)dy

dx= −y + lnx, y(1) = 10

5. Consider the Initial Value Problem

dy

dx= x2 − 3x2y, y(0) = 1

(a) Classify the DE. (i.e. state order and if linear or non-linear)

(b) Find all solutions to the differential equation.

(c) Apply the initial condition.

(d) Identify the transient and steady-state terms in the solution from part (c).

(e) On the same axes, give a quick sketch of the transient solution, the steady-state solution,and the full solution (i.e. the sum of the two parts).

6. Look at the Wikipedia article on Brachytherapy.

Some types of cancers (such as in the lip) are treated by surgically implanting a radioactiveseed that emits radiation which in turn permanently damages the DNA in the cancer cells.Let A(t) denote the amount of Cobalt-60 in a seed at time t.

(a) Assuming the rate of radioactive decay is proportional to the amount of Cobalt-60 re-maining in the seed, write an IVP describing this problem with initial time t = 0.

(b) Solve your IVP.

(c) Given that the half-life of Cobalt-60 is 5.26 years, determine the proportionality constantyou introduced in part (a).

(d) What is the percentage of Cobalt-60 remaining in the seed after 1 year and after 10 yearsof implantation.

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Figure 4: An exam preparation handout for my Math 228 - Differential Equations for Physics and Chemistry course at theUniversity of Waterloo, Canada.

Math 228 Final Exam Review

You are responsible to know everything that was covered in this course. That is, all ma-terial covered in class, tutorial, on assignments (0 to 6), and in the textbook chapters 1 to7. Exceptions include exact equations (Ch. 2.4), the annihilator approach (Ch. 4.5), seriessolutions at singular points (Ch. 6.2), and time-domain vector DEs (Ch. 8)

The following are exam-type questions for practice.

1. Find the general solution of the following DEs.

(a) y′′ + 2y′ + 5y = e−x sin 2x

(b) y′′ − 4y = (x2 − 3) sin 2x

(c) y′′ − 2y′ + y = (x2 − 1)e2x + (3x+ 4)ex

(d) y′′ − 2y′ + y =ex

1 + x2

2. For the following, determine the Laplace or inverse Laplace transform as required.

(a) L

{∫ t

0

e−3τ cos(√2τ)dτ

}

(b) L {f(t)} where f(t) =

{2 0 ≤ t < 3−2 3 ≤ t < ∞

(c) L −1

{s

s2 − 10s+ 29

}

(d) L −1

{a

s(s2 + a2)

}

3. Solve the system of DEs by rewriting the system as a vector DE and using vectorLaplace transforms.

dx

dt= 4y + 1

dy

dt= 2− x

x(0) = 1, y(0) = 0

4. Solve the following initial value problems any way you choose.

(a) xy′′ − y′ = 1, y(0) = 1, y′(0) = −1

(b) y′y′′ = 4x, y(1) = 5, y′(1) = 2

(c) y′′ + 5y′ + 4y = 0, y(0) = 1, y′(0) = −1.

1

(d) 1 = y′ + 6y + 9

∫ t

0

y(τ)dτ , y(0) = 0

5. Solve the DE: y′′ − x2y′ + xy = 0.

6. The temperature T (r) in a circular ring around a campfire with inner radius 1 m andouter radius 3 m is governed by the DE

rd2T

dr2+

dT

dr= 0.

Solve the boundary value problem if T (1) = 40◦C and T (3) = 10◦C.

7. Classify and solve the following DEs.

(a) x2 dy

dx= y − xy

(b) xdy

dx− y = 2x2

(c) xdy

dx= y +

√x2 − y2, x > 0

(d) t2dy

dt+ y2 = ty

(e) x2y′′ − 7xy′ + 41y = 0

(f) x2y′′ + (y′)2 = 0

(g) (y′′)2 = y2

8. Two friends sit down to chat over a cup of coffee. When the coffee is served, theimpatient friend adds a tablespoon of cold cream to their coffee. The relaxed friendwaits 10 minutes before adding the same amount of cream (at the same temperature)to their coffee. The two friends now begin to drink their coffee. Using Newton’s Lawof cooling, determine who has the hotter coffee. We can safely assume that the creamis cooler than the air in the room. A discussion and a sketch is all that is required. Donot solve any DEs to answer this question. Use your reasoning skills only.

2



Figure 5: Student course evaluation summary for Math 228 - Differential Equations forPhysics and Chemistry course at the University of Waterloo, Canada.


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Figure 6: Student course evaluation comments for Math 228 - Differential Equations for Physics and Chemistry course at theUniversity of Waterloo, Canada.


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Figure 7: Student course evaluation summary and sample comments for Math 237 - Calculus 3 for Honours Mathematics courseat the University of Waterloo, Canada.



Figure 8: Student course evaluation comments for Math 237 - Calculus 3 for HonoursMathematics course at the University of Waterloo, Canada.


!

Dept of Applied Mathematics, University of Waterloo, Waterloo, Ont N2L 3G1 7 December, 2015 Job Title: Assistant Professor, Posting Number: F326PO Dear Search Committee, This is a letter of reference for Kathleen Wilkie who is applying for a tenure track Assistant Professorship at the University of Vermont. I will start by summarizing her academic credentials/achievements and then comment more specifically on her pedagogical skills. I should state at the outset that, in my opinion, she combines all the essential qualities that constitute an excellent academic. Kathleen obtained an honours undergraduate degree in Applied Mathematics with distinction, graduating on the Dean's Honour List. She obtained her Master's degree in Applied Mathematics (on "Localised medical image registration") under the supervision of Professor E.R. Vrscay in 2005. Kathleen carried on to complete her PhD under my supervision on "Cerebrospinal fluid pulsation and aging effects in mathematical models of hydrocephalus". Her performance, as a graduate student, continued at the very high level established during her undergraduate days. A glance at the four courses Kathleen took for credit (as part of the PhD program requirements): Asymptotic Analysis (97%), Dispersive and Nonlinear Waves (88%), Advanced PDEs (96%), Waves in Porous Media (94%), is an indication of the A+ standing that she managed to maintain throughout her graduate career. Her graduate record speaks for itself - she was awarded numerous scholarships (notably the NSERC graduate scholarships for both her Master's and PhD). Kathleen's interests are broad as evident from her thirteen plus publications to date. She wrote an excellent thesis and successfully defended it in August 2010. As mentioned earlier, Kathleen's PhD research focused on mathematical models of hydrocephalus. She tackled this clinical problem using the mathematical theories of poro-elasticity and viscoelasticity. Using the latter, she successfully addressed the question of


!

whether the pulsations of cerebrospinal fluid in the cerebral ventricles, could be a possible mechanism for ventricular expansion (a question that has been actively debated in the neurosurgical literature in recent years). She extended this work in four further publications to cover large deformations, and addressed the longstanding and challenging question of what mechanisms give rise to "normal pressure hydrocephalus". Kathleen’s postdoctoral work involved closer interdisciplinary collaboration with cancer biologists and clinicians at the Center of Cancer Systems Biology at Tufts University. Her focus there, has been on the development of mathematical models of immune-tumour dynamics and low dose radiation. Although this appears to be a significant departure from her PhD work, the mathematical methodology and approach is, in fact, very closely related to approaches she developed in her PhD work on mathematical models of hydrocephalus. Her transition into working on cancer systems biology has been rapid and extremely successful, and she has over five publications in this field, to date. She has thus developed a facility with and expertise in population dynamics through her research work on the cancer-immune system. Further, her expertise overlaps with the broad field of computational biology, especially with respect to her current research work on an agent-based model for the development of cancer in the breast tissue structure - which I believe she hopes to link up with tissue biomechanics at a later stage. Kathleen’s other more recent work in systems biology attempts to link gene expression to protein expression and pathway analysis, and to integrate this into a population-level mathematical model, for the intercellular signaling involved in cancer cachexia. At the same time her research interests in hydrocephalus have continued unabated, and her research accomplishments in this field are only now receiving the recognition that they fully deserve (she was recently one of a handful of speakers invited to deliver an hour long presentation at the “1st CSF Hydrodynamics Symposium” held at ETH, Zurich). She has given over seven invited presentations at conferences and workshops, as well as a number of contributed presentations, and has also been active in conference/workshop organization. As part of the PhD requirements, a PhD-candidate is also required to teach a one-semester course at the undergraduate level. By all accounts, she is an excellent teacher, and thus had completed two such assignments for the Department by the end of her PhD program! She defended her thesis with great tenacity and enthusiasm, all of which confirmed to me further, that she would be a most effective and stimulating teacher. In fact, after her successful defense of her PhD thesis, Kathleen was immediately hired to teach two math service courses (these were courses taught to engineering students) in the subsequent term, before departing for her postdoctoral work at Tufts University. All four courses that she taught, while at Waterloo, were extremely well received by the students and resulted in excellent student evaluations – had she been in a tenure track position,


!

they would have provided an excellent launching-pad for a distinguished teaching award! Apart from second and third year applied math courses, Kathleen is extremely at ease teaching the typical first year sequence of calculus and linear algebra courses, with the added bonus that she is an enthusiastic and engaging teacher. Apart from her academic pursuits, Kathleen also has a notable record of professional service, which include Graduate Student Association Departmental Councillor (2005-2009), Mathematics Faculty Graduate Student Representative (2006-2008) and Graduate Student Senator (2007-2009) amongst others. Although a little reserved by nature, Kathleen has a pleasant personality and organised "pot-luck" dinners (during her time as a graduate student) and other social get-togethers for her fellow graduate students, faculty and staff. In fact, during her time as a graduate student, she contributed in no small measure to the congenial and sociable atmosphere that exists in my research group and indeed in the graduate student body in applied mathematics as a whole. I imagine Kathleen would fit seamlessly into your outreach activities, and would be an excellent and inspiring advocate for recruiting more girls into the mathematical sciences. I hope the above has given you a clear picture of the very strong research program, that Kathleen has managed to establish over the past five years. To my mind, this is clear evidence of an emerging researcher with a clear ability to establish and maintain an independent, externally funded research program. She has extensive experience collaborating with research hospitals, and has collaborated with researchers at The Hospital for Sick Children and Sunnybrook & Womens Hospital (during her PhD work). In addition, during her postdoctoral work, she worked in a research hospital and so has managed to establish broad connections and collaborations with researchers at the Tufts School of Medicine in Boston as well. Thus, in conclusion, I recommend Kathleen very strongly for the position at your Institution. As a strong researcher in the interdisciplinary field of mathematical biology/medicine, she also brings a very different and refreshing perspective to teaching (even to non-mathematics majors), both with respect to first year courses and higher level courses. She has all the attributes and pedagogical skills that constitute an excellent teacher and mentor – one who would inspire and engage the students in mathematics courses. In addition, her ability and enthusiasm to encourage more women into the field of mathematics, and to act as an exemplary role model, is highly commendable and an additional benefit of hiring an individual like Kathleen onto your faculty.


!

Yours sincerely, Siv Sivaloganathan === Professor of Applied Mathematics, University Research Chair, University of Waterloo, Waterloo, Ont N2L 3G1 & Director, Centre for Mathematical Medicine, Fields Institute, Toronto, Ont M5T 3J1 !!


University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

519-888-4567

http://www.uwaterloo.ca

10 August 2015

Dear Committee,

This letter is written to address the teaching capabilities of Kathleen Wilkie, who taughtcourses in the Faculty of Mathematics from January 2008 until December 2010. In thatcapacity, she taught four courses in the Faculty of Mathematics.

The three courses taught by Dr. Wilkie were MATH 127 (Calculus I for the Sciences),MATH 138 (Calculus 2 for Honours Mathematics), MATH 228 (Differential Equationsfor Physics and Chemistry), and MATH 237 (Calculus 3 for Honours Mathematics).Students in these courses evaluate their instructors in a variety of matters on a five-point scale, and the average results are reported out of five points, with higher numbersdenoting a stronger evaluation. Evaluation forms are distributed in class, late in theterm, and the students are given 10-15 minutes to complete the evaluations. Dr. Wilkie’sevaluation scores for “effectiveness of teaching” are summarized in the following table:

Term Course Effectiveness Response rate Course averageWinter 2008 MATH 138 3.84 40% 4.20Winter 2009 MATH 127 3.96 48% 3.72Fall 2010 MATH 228 4.00 66% 4.09Fall 2010 MATH 237 3.98 48% 4.07

To put this data into context: the course averages are measured over 55-67 offerings ofeach course (except MATH 228, which is measured over only 8 offerings), and class sizesin Dr. Wilkie’s lectures varied from about 50 in MATH 228, to nearly 200 in MATH127. Course averages in the table are calculated over all offerings, regardless of the term.The winter offering of MATH 127 is usually populated with a large number of repeaterswho did not perform well in MATH 127 in the previous fall term, which is reflected inthe lower average evaluation numbers for that term. Dr. Wilkie nevertheless performedquite well in that term, which speaks highly of her ability to inspire weaker students.

This data suggests that Dr. Wilkie is an effective teacher of mathematics. I have notpersonally witnessed a lecture of Dr. Wilkie’s. However, I interacted with her in myposition as Associate Dean for Undergraduate Studies many times, and she impressedme with her thorough preparations. I am confident that she will perform well wherevershe teaches.

In summary, Dr. Wilkie is a very good instructor of mathematics. I definitely recom-


mend her to anyone as a university level mathematics teacher.

Sincerely,

David McKinnonProfessor of Pure Mathematics

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