Mathematical underpinnings of Economics presented in a chronological manner as to the developments of the math and the applications to economics.

1. Economics
Structure of the Science

2. Science
The invention of
deliberately
oversimplified theories
is one of the major
techniques of science,
particularly of the
“exact” sciences which
make extensive use of
mathematical analysis.
John Williams The
Compleat Strategyst

3. Underlying Mathematics
• Geometry
• Algebra
• Analytic Geometry
• Linear Algebra
• Linear vs. Logarithmic
• Calculus
• Game Theory
• Statistics
• Computer algorythms

4. The justification of all
mathematical models
is that, oversimplified, unrealistic, and even
false as the may be in some respect, they
force analysts to confront possibilities that
would not have occurred to them otherwise.
The history of physics and medicine abounds
with wrong or incomplete theories that throw
just enough light to allow some other big
breakthroughs. The atom bomb, for example,
was built before physicists understood the
structure of particles.

5. The Ideal Model
• The effort to put
Economics on a
rigorous
mathematical footing
like Newton’s
mathematization,
using his invention of
the calculus, of
physics.

6. Geometry
Geometry (Ancient Greek:
γεωμετρία; geo- "earth", -metria
"measurement") is a branch of
mathematics concerned with
questions of shape, size, relative
position of figures, and the
properties of space. Geometry is
one of the oldest mathematical
sciences. Initially a body of
practical knowledge concerning
lengths, areas, and volumes, in
the 3rd century BC geometry was
put into an axiomatic form by
Euclid, whose treatment—
Euclidean geometry—set a
standard for many centuries to
follow

7. Algebra
• Algebra is the branch of
mathematics
concerning the study of
the rules of operations
and relations, and the
constructions and
concepts arising from
them.

8. Algebra
• While the word algebra comes
from the Arabic language (al-jabr,
‫الجبر‬ literally, restoration) and
much of its methods from
Arabic/Islamic mathematics, its
roots can be traced to earlier
traditions, which had a direct
influence on Muhammad ibn
Mūsā al-Khwārizmī (c. 780–850).
He later wrote The Compendious
Book on Calculation by
Completion and Balancing, which
established algebra as a
mathematical discipline that is
independent of geometry and
arithmetic.

9. Analytic Geometry
In classical
mathematics, analytic
geometry, also known
as coordinate
geometry, or Cartesian
geometry, is the study
of geometry using a
coordinate system and
the principles of algebra
and analysis

10. Analytic Geometry

11. Calculus
• Calculus is the study of
change,in the same way
that geometry is the
study of shape and
algebra is the study of
operations and their
application to solving
equations.

12. Calculus

13. Game Theory
• Game theory is a
mathematical method
for analyzing calculated
circumstances (games)
where a person’s
success is based upon
the choices of others.
• 1944 book Theory of
Games and Economic
Behavior, with Oskar
Morgenstern

14. Game Theory/Nash Equilibrium
• Stated simply, Amy and
Phil are in Nash
equilibrium if Amy is
making the best
decision she can, taking
into account Phil's
decision, and Phil is
making the best
decision he can, taking
into account Amy's
decision.

15. RAND Corporation
• R and D
• Original Think Tank to
come out of WW II
• Adopted and advanced
Game Theory and
applied it to military,
political and economic
problems

16. Econometrics
• Data Collection
• Analysis
• Statistical techniques
• Regression Analysis
– Demand Curves
– Supply Functions
– Elasticity
• Models

17. Computers and Super Number
Crunching
• Modeling
• Big Data
• Forecasting
• Analysis
• Flash Trading

18. Managerial Economics
• Mathematics are tools that provide a
structure for analysis.
• Economics is the science of making decisions
in the presence of scarce resources.
• Managerial Economics is the study of how to
direct scarce resources in the way that most
efficiently achieves a managerial goal.

19. Let’s Get Busy