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BMI web in its page: Why-Me? <br>
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<h4 align="center">I Am a Mathematician</h4>
<p align="left">The brain is one of the most important and
interesting subjects for mathematics. We regard the brain as a
mathematical subject since mathematics is a discipline for
quantity, structure, space, and change. The precision of concepts
and the rigor in analysis are two important feature of
mathematics. The brain calls for a new kind of mathematics. The
emergent structures of the brain could lead to a new mathematical
subject of "emergent structures" (e.g., emergent functional) as
opposed to pre-specified structures (e.g., pre-specified basis
functions). The domain of a function emerges and adapts, and so
does the co-domain (range). The spatial and temporal attention
mechanisms in the brain tell us that the source of the domain that
the function depends on dynamically change very quickly. The
brain-like optimization seems to provide a general-purpose
solution to problems in the nonlinear dynamic systems, stochastic
processes, sparse coding, mathematical nonlinear optimization,
statistical learning theory, and much more. How the brain figures
out low dimensional nonlinear manifolds incrementally in
uncertainty while avoiding the rigidity of probability would
likely extend the existing frameworks of probability and
functional analysis in mathematics.</p>
<h4 align="center">Why Learning Mathematics?</h4>
<p align="left">The brain is a physical object that is governed by
physical quantities, structures, spaces, and changes, which are
exactly what mathematics is about. For the same reason,
theoretical physics uses much mathematics. Since the brain-mind is
more complex than more basic physical properties, such as force,
mass, speed, and time, the need of mathematics for brain-mind
research is more obvious. The basic mathematical subjects
necessary for understanding the brain-mind include, but are not
limited to, mathematical analysis, vector analysis, linear algebra
(e.g., eigenvectors and eigenvalues), calculus-based
multi-dimensional probability, real analysis (e.g., measure),
functional analysis (e.g., random vectors, random matrices, limit
and convergence in vector space, representation of functionals,
nonlinear approximation, nonlinear optimization), mathematical
statistics (e.g., statistical efficiency). Some experimental
biologists, neuroscientists and psychologists have learned
non-calculus-based probability and statistics, which are useful
for them to analyze their own experimental data but insufficient
for understanding the brain-mind. </p>
<pre class="moz-signature" cols="72">--
--
Juyang (John) Weng, Professor
Department of Computer Science and Engineering
MSU Cognitive Science Program and MSU Neuroscience Program
3115 Engineering Building
Michigan State University
East Lansing, MI 48824 USA
Tel: 517-353-4388
Fax: 517-432-1061
Email: <a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:weng@cse.msu.edu">weng@cse.msu.edu</a>
URL: <a moz-do-not-send="true" class="moz-txt-link-freetext" href="http://www.cse.msu.edu/%7Eweng/">http://www.cse.msu.edu/~weng/</a>
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