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Nancy Kopell

Nancy Kopell is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nancy Kopell rather than just read about it. In short: Nancy Jane Kopell (born November 8, 1942, New York City) is an American mathematician and professor at Boston University. She is co-director of the Center for Computational Neuroscience and Neural Technology (CompNet).

Key takeaways

  • Nancy Kopell belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Nancy Kopell to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Nancy Kopell from memory before moving on to harder problems.

Reference excerpt

Nancy Jane Kopell (born November 8, 1942, New York City) is an American mathematician and professor at Boston University. She is co-director of the Center for Computational Neuroscience and Neural Technology (CompNet). She organized and directs the Cognitive Rhythms Collaborative (CRC). Kopell received her B.A. from Cornell University in 1963 and her Ph.D. from Berkeley in 1967. She held visiting positions at the Centre National de la Recherche Scientifique in France (1970), MIT (1975, 1976–1977), and the California Institute of Technology (1976). The focus of her research is the field of applied biomathematics and includes use of mathematical models to analyze the physiological mechanisms of brain dynamics. The techniques Kopell uses include extensions of invariant manifold theory, averaging theory, and geometric methods for singularly perturbed equations. From the peak of her career in 1990, she has contributed to over 200 published research articles in the field of biomathematics. Her current interests include topics such as: how does the brain produce its dynamics (physiological mechanisms), how do brain rhythms take part in cognition (sensory processing, attention, memory, motor control), and how can pathologies of brain dynamics help to understand symptoms of neurological diseases (Parkinson's disease, schizophrenia, epilepsy) as well as altered states of consciousness (anesthesia). She collaborates widely with experimentalists and clinicians in order to conduct research on these topics. Kopell is a 1990 MacArthur Fellow.

Biography

Early life and education Kopell was born on November 8, 1942, and grew up on Pelham Parkway in the Bronx. Her father was an accountant and her mother and older sister also majored in mathematics. As a child, she had a severe eye problem which taught her how to cope with being "different." This ability to cope would help her successfully deal with feelings of marginalization she would later experience as a female scientist. She attributes her professional success to this ability as well as the support she received from mentors throughout her career. Her high school teachers encouraged her to go into the mathematics field. During her undergraduate education at Cornell University, she registered for a mathematics honors program, and was the only female participant. Kopell graduated from Cornell with an A.B. in 1963. She then decided to attend graduate school in order to "find an alternative to the more traditional life her family expected for her." Kopell originally applied to programs on the East Coast and was admitted to all of them except for one; however, after being encouraged by another student, she chose to attend school on the West Coast instead. She was admitted to the University of California, Berkeley, with a fellowship and graduated with an M.A. and a Ph.D. in 1967. At Berkeley, she did well on her exams and was known as the "bright female." However, she struggled in the early stages of her dissertation work and switched supervisors to Stephen Smale. Smale suggested a problem which Kopell almost singlehandedly solved, leading to her thesis in the field of dynamical systems which catapulted her career.

Academic career After completing her graduate education, Kopell accepted an instructorship at the Massachusetts Institute of Technology. There, she met collaborator Lou Howard, with whom she published several articles. She later met her husband, Gabriel Stolzenberg, at Northeastern University. While Kopell did her thesis work in theoretical mathematics, she later switched to applied mathematics. In 1969, she joined Northeastern University as faculty, becoming a full professor in 1978. In 1986, she became a professor of mathematics at Boston University and in 2009 she became the first woman at Boston University to be named a William Fairfield Warren Distinguished Professor. She was awarded a MacArthur Foundation Fellowship in 1990 for her work developing methods of dynamical systems to attack problems of applied mathematics. She is currently Director and Co-Founder of the Cognitive Rhythms Collaborative, which consists of a group of over two dozen labs, mostly in the Boston Area, working on brain dynamics and their cognitive implications. She is also Co-Director of the Center for Computational Neuroscience and Neural Technology (CompNet). Kopell is a member of the National Academy of Sciences and the American Academy of Arts and Sciences. She was recently selected to be an honorary member of the London Mathematical Society, a distinction given to one or two mathematicians per year worldwide. She has been awarded Sloan Guggenheim, and McArthur Fellowships, and has an honorary Ph.D. from the New Jersey Institute of Technology. She has given the Weldon Memorial Prize Lecture (Oxford), the von Neumann Lecture, and the Josiah Willard Gibbs Lecture (AMS), as well as multiple other named lectureships.

Honors and memberships 1975 Sloan Fellowship 1984 Guggenheim Fellowship 1990 MacArthur Fellowship 1996 National Academy of Sciences 1996 American Academy of Arts and Sciences 1999 Josiah Willard Gibbs Lecture (American Mathematical Society) 2006 Weldon Memorial Prize (Oxford) 2007 John von Neumann Lecture (Society for Industrial and Applied Mathematics) 2009 Fellow of the Society for Industrial and Applied Mathematics 2011 Honorary Member of the London Mathematical Society 2013 Jürgen Moser Lecture 2015 Israel Brain Technologies Mathematical Neuroscience Prize 2015 Fellow of the American Mathematical Society 2016 Swartz Prize

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Nancy Kopell

Start with the simplest possible case. Write down what Nancy Kopell claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nancy Kopell before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nancy Kopell ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nancy Kopell

In research
Nancy Kopell appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Nancy Kopell in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Nancy Kopell is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Nancy Kopell outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Nancy Kopell in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Nancy Kopell means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Nancy Kopell out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nancy Kopell in simple terms?

Nancy Jane Kopell (born November 8, 1942, New York City) is an American mathematician and professor at Boston University. She is co-director of the Center for Computational Neuroscience and Neural Technology (CompNet).

Why does Nancy Kopell matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nancy Kopell?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nancy Kopell.

Tags

  • 1942 births
  • 20th-century American mathematicians
  • 20th-century American women mathematicians
  • 21st-century American mathematicians
  • 21st-century American women mathematicians
  • American neuroscientists
  • American women neuroscientists
  • Boston University faculty
  • Cornell University alumni
  • Fellows of the American Academy of Arts and Sciences
  • Fellows of the American Mathematical Society
  • Fellows of the Society for Industrial and Applied Mathematics

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