Algebra, Arithmetic and Geometry
-- With a View Towards Applications /2005
This is a special "Long-Course" entitled "Algebra, Arithmetic and
Geometry - with a View Toward Applications" commencing from September
2005. This course is open to all students / faculty who are interested
in Mathematics. The main aims of this Course are to make students think,
stimulate them into active learning, show them the excitement of doing
mathematics on their own, enthuse them into learning more advanced topics
with confidence, assist them to realize their potential, nurture their
Mathematical talent and appreciate the deep effects on the application
world. Special effort will be made to encourage the participants to ask
questions, raise doubts and seek clarifications in the class-room.
The course will be taught very much in the spirit of a mathematical
"guided tour" Volunteering as the guide, I take upon myself the task
of charting a route through beautiful mathematics surrounding the
above three classical branches and lead the audience through the route
pointing out the beautiful sceneries and historical landmarks along the
way. The emphasis will be given to motivate the development of important
concepts using as many examples as possible. These examples will range
from routine to fairly sophisticated theoretical ones.
This course will ONLY presuppose a basic knowledge of Elements of
set-theory, Elementary abstract algebra and linear algebra. The first
stage of the course will be the foundations of " Algebra", Arithmetic
(Number theory) " and " Geometry " and interplay among them. Some topics
to be covered are listed below. Depending on the background/interests
of the participants, special topics other than those mentioned below
could also be covered.
This is a special "Long-Course" entitled "Algebra, Arithmetic and
Geometry - with a View Toward Applications" commencing from September
2005. This course is open to all students / faculty who are interested
in Mathematics. The main aims of this Course are to make students think,
stimulate them into active learning, show them the excitement of doing
mathematics on their own, enthuse them into learning more advanced topics
with confidence, assist them to realize their potential, nurture their
Mathematical talent and appreciate the deep effects on the application
world. Special effort will be made to encourage the participants to ask
questions, raise doubts and seek clarifications in the class-room.
The course will be taught very much in the spirit of a mathematical
"guided tour" Volunteering as the guide, I take upon myself the task
of charting a route through beautiful mathematics surrounding the
above three classical branches and lead the audience through the route
pointing out the beautiful sceneries and historical landmarks along the
way. The emphasis will be given to motivate the development of important
concepts using as many examples as possible. These examples will range
from routine to fairly sophisticated theoretical ones.
This course will ONLY presuppose a basic knowledge of Elements of
set-theory, Elementary abstract algebra and linear algebra. The first
stage of the course will be the foundations of " Algebra", Arithmetic
(Number theory) " and " Geometry " and interplay among them. Some topics
to be covered are listed below. Depending on the background/interests
of the participants, special topics other than those mentioned below
could also be covered.
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