The Subtleties of Subversion

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The Subtleties of Subversion

• Eric Marland
• Appalachian State University

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Outline

• A Brief Background
• General Strategies
• Specifics
• Conclusions

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Development of Mathematics in Biology(a very
small glimpse)

1789 Thomas Malthus Compared growth rates of
populations with food production and provided the
motivation for Darwins theory of natural
selection.
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Quetelet (1796-1874) and Verhulst (1804-1849)
Introduced the idea of diminished growth rates
with increases in population
Lotka (1907) and Volterra (1926) foundations of
predator-prey dynamics
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• Other Notable Advances
• Pearl (epidemiology - pop) and Reed 1908
• Kermack and McKendrick 1927 - SIR
• Nicholson, Bailey 1935 competition models
• Leslie 1945 matrix models of populations.

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Maud Menten one of the first women doctors in
Canada (1911) and perhaps the first use of
electrophoresis in separating proteins (1944).
Leonor Michaelis along with Menten
characterized enzyme catalyzed reactions (1910).
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The foundations of pde models in biology
originate in the early 1900s with K. Pearson and
J. Blakeman. One of the most notable example is
from Sir Ronald Fisher because it attracted
attention from both geneticists and
mathematicians.
R.A. Fisher (1890-1962) pushed the limits of
modern statistics and genetics, introducing the
concepts of analysis of variance, randomization,
and likelihood. He also introduced us to
Fishers equation for biological invasions, one
of the earliest models shown to exhibit traveling
wave solutions (proved by Kolmogorov 1937).
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A.V.Hill Nobel prize in 1922 concerning
production of heat in muscles. Also contributed
to the theory of nerve conduction.
Bernhard Katz Nobel Prize in 1970 concerning
advances in neuromuscular interaction. A student
of A.V. Hill
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Hodgkin and Huxley 1963 Nobel Prize concerning
chemistry of nerve conduction (work done in the
1950s). Hodgkin calculated solutions to their
model equations on a crank hand
calculator. Huxleys work on theories of muscle
contraction, together with Einsteins work on the
relationship between diffusion and Brownian
motion, forms the basis for most molecular scale
molecular motor models.
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Boris Belousov found the first oscillating
chemical reaction (1951). Rediscovered by Anatol
Zhabotinski in 1964.
Anatol Zhabotinski is currently an adjunct
professor at Brandeis University.
The discovery of oscillating chemical reactions
led to Alan Turings famous The Chemical Basis
for Morphogenesis, Turings only paper
concerning biology.
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Classical Mathematics

• Algebra
• Topology
• Analysis
• Differential Equations
• The Dark Side (Applied Mathematics)

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Classical Biology

• A standard historical practice of research
  biology
• was to describe the features of organisms in
  order
• to gather sufficient data to construct a
  conceptual
• model - Julius Jackson (from that book youve
• been carrying around)
• The Dark Side (Theory and Statistics)

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Curriculum or Culture?

• Increasing quantitative skills
• Increase quantitative awareness
• Increase interaction between fields
• Increase communication between fields
• Increase biological awareness

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Insulting your Colleagues

• Some mutations happen faster than others
• Small changes can make big differences.
• Incremental changes (in culture) are easier to
  achieve than large changes.
• Devaluing someones field wont necessarily make
  them your friend.

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Expertise

• Clear and Concise Goals
• Collaboration
• Consultants
• Community

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Goals

• How many theoretical biologists do you know who
  have only biology degrees?
• Will the students learn better?
• Will the students be more marketable?
• What is the ideal?
• What is realistic?

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Developing a Community

• MAA / PREP www.maa.org
• SMB www.smb.org
• NCSI www.computationalscience.com
• BioQUEST www.bioquest.org
• BEN
• NCBI

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How do we collaborate?

• Use a common language or framework
• Let go of preconceived notions about content
• Have flexibility and understanding about other
  dept. structures and culture.

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Content decisions

• What should students
• Master, understand, be exposed to, be aware of in
  light of the student population
• Types of experiences - lab, theory, computation,
  discussion, debate
• Reinforcement of the disciplines importance

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Course Structure

• Organizing content
• When do you need ANOVA
• When do you need Organic Chemistry
• Where can you reinforce derivatives
• Dealing with transfer students
• How much will a transfer student have to retake?
• When do students see real biology?

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Challenges for the teacher

• Use of technology

• Taking Risks in front of others students and
  colleagues
• Letting go of being the absolute expert

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Measuring Success

• Has the culture changed?
• Will the program continue and grow?
• Have the students benefited?
• Have you gone nuts?

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Difficulties

• Space allocation
• Administrative and political details
• Impatience and Ambition
• Time

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(No Transcript)
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Basis for Change

• BIO2010
• MAA - CUPM
• Math Bio 2010
• Be careful of these guides

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Specifics

• Introductory Mathematics
• Introductory Statistics
• Course Structure
• Course Content
• Pulling it together

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Bio-calculus Assignment

• Read the selections of BIO 2010
• From SCIENCE magazine in an assigned year, report
  on an article on a topic of interest. 
• The report must contain the following
• A summary of the article.
• A summary of the mathematics used in the
  research.
• A specific outline of the mathematics used in the
  article itself.
• A reflection on how the article pertains to BIO
  2010.

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Responses

• In reading an article from the well-known
  magazine Science, I discovered myself why
  mathematics is important in science and how much
  it pertains to it. The article that I read
  pertained to gamma oscillations and object
  processing in the infant brain

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• One point I really agreed with was, Teaching
  Materials and Faculty Development Standard texts
  either need to be revised or replaced by more
  quantitative texts.

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Course Content

• Terminology and Syntax
• Technology
• Software packages (demo, practice, mastery)

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Introductory Mathematics

• Guest speakers to reinforce the importance
• Computer laboratories
• Biology motivated content
• Meshing technology to maximize utility
• Remember that it is still a math course

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Purpose of the course

• Form the foundation for the interplay between
  mathematics and biology
• Introduce the common language for quantification
• Prepare students for future biology classes
• Prepare students for future mathematics classes
• Demonstrate the connections between biology and
  mathematics

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Guest Speakers

• Fosters town-gown relations.
• Eric, thanks for inviting me it was
  invigorating! Troy asked a question I was not
  prepared to answer Didnt mean to short change
  him Dan
• Reinforcing non-academic support of quantitative
  skills.

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Technology

• Simple tools
• Start-up costs vs. lasting use
• Interdisciplinary links (what are other
  departments using?)
• Coordinating across departments

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Elements of the course

• Freshman Learning Communities Biology
  motivation/inspiration
• Guest speakers
• Lab experiences
• Technology

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Introduction to Derivatives

• Using data as motivation
• Making intuitive links to the derivative
• Difference equations to derivatives
• futurepresentchange

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Modeling

• Discrete vs. Continuous
• Validity of a model (when is discrete app)
• Conceptual foundations for derivatives

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Integral Calculus

• Accumulations of change vs. areas
• Solving differential equations vs. integrals
• Riemann Sums and discrete data
• Numerical solutions and difference equations

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The Calculus Cycle
Decrease time step
Difference equations
Derivatives
Numerical Solutions
Reverse Solutions
Differential equations
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Student Perception

• I can understand mathematics better when put in a
  biology context.
• Disagree-41 Neutral-22 Agree-37

Mathematics is Important to the field of
Biology. Disagree-0 Neutral-15
Agree-85 Knowing more mathematics will help me
in my future career. Disagree-0 Neutral-19
Agree-82
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• Thanks for inviting me - it was invigorating!
  -guest speaker
• I especially enjoyed the dinner at Gary's house
  with your students - consultant
• I really like (now) how the math and biology
  curriculums are integrated because I feel that
  the math portion has some direction towards what
  Im interested in. - student

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• I believe that this course is teaching me more
  than any of the other courses. It lets me know
  that math is related to al fields and that
  knowing these situation and types of solutions
  will be good for me in the future - student

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Introductory Statistics

• How much time do you have?
• What topics do you need in biology classes?
• What can you split up if you dont have time?
• Remember that it is still a statistics course.

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The Biology Curriculum

• Prerequisites in courses
• Ordering of courses
• Gatekeeper courses
• Reinforcing the mathematics

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Pulling it all Together

• Capstone Opportunity
• Research experience
• Project-based course
• Research Experiences
• When can students participate?
• How many can participate?

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Lessons Learned

• Baby Steps
• Reinforcement of each discipline
• Patience
• Administrative support
• Keep reaching (where will you go next?) (future
  goals to build off of current goals.

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What are the future goals

• Cross disciplinary faculty
• Integrated coursework - changing the culture
• High school curriculum - changing the culture
• Sharing ideas and developing a community
• Mathematical Stuffiness - changing from a
  client-discipline standpoint to a sub-field view.

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Dissemination

• How do you tell everyone else about what you have
  done?
• Shameless Advertising
• MAA-PREP / NCSI joint workshop next summer at
  Harvey Mudd on Computational and Mathematical
  Biology