AMIS 3600H Accounting Information Systems
Spring 2015
Office hours: MW 10:30 – 11:00
John Fellingham
Fisher 406
General Description
The course deals with theory and practice in the academic discipline of accounting. In
particular, accounting will be treated as an information science. That is, not only is
accounting a conveyor of information, the accounting activity, itself, resides in an
environment in which information is a first order phenomenon. Accounting affects, and
is affected by, the information environment.
Sometimes accounting is treated as a measurement science. That is, the presumption is
there exists an underlying true state of the world to be identified. That is not the
perspective undertaken here. In an information science, as evidence is gathered, state
probabilities are consistently revised. Probabilities are always in view, and “true state of
the world” is not a useful construct.
Earlier versions of the course textbook had as the objective the accumulation of several
information theorems, and then relating them to accounting. In a way, that is still the
case. But as revisions take place, one theorem, in particular, has occupied a central and
unifying role. The mutual information theorem establishes the equivalence of probability
measures of information with optimal growth rates (and dollar values) of general
investment activity. The investment activity is general in the sense that it includes
activities of economic organizations like firms, as well as investing in already existing
securities. In fact, as we shall see from proofs of the theorem, it is probably more
applicable to non-market (firm) activity.
Accounting is on the dollar side of the theorem’s equality; probabilities and information
science are on the other. The theorem, then, establishes the equivalence of accounting
and information science.
Given the mutual information theorem’s central role, it is tempting to start our inquiry
with the theorem, itself. There are reasons, however, not to do so. One reason is the
necessity of building appropriate intellectual foundations for development and
appreciation of the theorem. The first two theorems we encounter, then, will be the
fundamental theorem of linear algebra and the theorem of the separating hyperplane
(known as the fundamental theorem of finance when in an economic setting).
Both of the foundational theorems will be developed in the context of accounting
problems. Besides contributing to our intellectual foundations, the accounting problems
are interesting in their own right (at least to some people).
After the preliminary work the mutual information theorem is developed and proved. We
will do exercises to acquire facility with the logic, and, more importantly, gain
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appreciation for implications. For example, the theorem implies some statements about
social welfare.
The mutual information theorem allows access to Shannon’s most important theorem: the
noisy channel theorem about (error-free) transmission of information through any
inherently disruptive medium. Claude Shannon is the founder of information theory. In
fact, it is not difficult to find statements comparing Shannon’s achievements, both in
terms of intellectual elegance and effects on modern life, to those of Einstein. Some
examples are contained in the recommended reading material later in the syllabus.
The flip side of error correction is encryption. Several theorems are useful including
ones due to Fermat, Euler, and Euclid, as well as the fundamental theorem of arithmetic.
Coding and encryption technology lead naturally to quantum information and quantum
computation. Quantum encryption is apparently on the frontier of encryption technology.
A coding problem is solved using quantum processes.
A final topic employs quantum axioms to analyze the information environment,
especially in a production setting. We are particularly interested in an environment in
which information is used efficiently, and a distinct synergy arises. Accounting
measurement, even when it is not the primary source of the information, interacts with
the information environment, and can enhance, or corrode, synergy.
Text
All of the exercises and the suggested readings are from the textbook entitled
Accounting: An Information Science available on the course website.
http://fisher.osu.edu/~fellingham_1/523/index.html
The textbook (as of this writing) consist of 13 chapters:
1.
Accounting as an information science
2.
Alternative representations of the double entry system
3.
Accounting as a communication channel
4.
Theorem of the separating hyperplane
5.
Accounting and equilibrium: valuation in the row space
6.
Accounting stocks and flows
7.
Information stocks and flows
8.
Entropy
9.
Error detecting and error correcting codes
10.
Secret codes
11.
Quantum cryptography
12.
Production, synergy, and accounting
13.
Ross recovery theorem
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Recommended reading (optional)
Fortune’s Formula by William Poundstone
The Smartest Guys in the Room by Bethany McLean and Peter Elkind
When Genius Failed by Roger Lowenstein
Probability Theory: The Logic of Science by Ed Jaynes
Information Science by David Luenberger
Information Theory by Thomas Cover and Joy Thomas
A Mathematician’s Apology by G. H. Hardy
Alan Turing: The Enigma by Andrew Hodges
Course Requirements and Grading
Grades will be assigned based on cumulative performance in the course, using the
following weights for the components:
Making a positive contribution
to the learning environment
Comprehensive final exam
50%
50%
Examination
The final exam is comprehensive, closed book, and closed note. Calculators are allowed,
personal computers and other electronic devices are not. The final will be given at the
time determined by the University.
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Preliminary schedule for AMIS 3600 Spring 2015:
Topics
Readings
Problems
Introductory remarks
Skim
Ch. 8 (alternative)
Exercise
Directed graph and linear
representations of accounting
Ch. 1
Ch. 2.1 – 2.4
Exercises1.1, 1.2, 1.3
Example 2.1
Accounting as a
communication channel
Ch. 3.1 – 3.2
Examples 3.1, 3.2
Computing yrow
Ch. 3.2 – 3.5
Examples 3.2, 3.3, 3.4, 3.5
Fundamental theorem of linear
Ch. 3.8
algebra
Multiple loops
Ch 3.9
Example 3.8
Exercises 3.1, 3.3, 3.5, 3.9*
Chapter 3 exercises
“simple” example
Theorem of the separating
hyperplane
Ch. 4.1
Accounting illustration of the
theorem
Ch. 4.2 – 4.3
Arbitrage free pricing
Ch. 4.4
State probabilities*
Ch. 4.5
Multiple equilibria
Ch. 4.6
Example 4.1
Example 4.2
Example 4.2 (cont.)
“expanded” example
Exercises 4.1, 4.3, 4.4, 4.10
Ch. 4 exercises
Arbitrage opportunities and
horse racing*
Exercises 4.5, 4.6, 4.7
Continuous compounding and
Ch. 6.1.1
e
Exercises 6.18, 6.19
Exercise 8.23*
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Long-lived assets,
amortization, and economic
income
Example 6.1
Ch. 6.1.3, 6.2
Steady state accounting
Ch. 6.3
Example 6.1 (cont.)
Exercises 6.2, 6.9
Exercise 6.6
Accounting for leases
Entropy – Shannon’s theorem,
additivity, and mutual
Ch. 8.1.1
information
Example 8.1
Example 8.2, 8.3
Kelly criterion
Ch. 8.1.2
Fundamental theorem of
accounting - conditions
Ch. 8.2
Accounting rate of return
Ch. 8.3
Example 8.4
Social welfare and the
fundamental theorem of
accounting
Example 8.5
Ch. 8.4
Maximum entropy probability
Ch. 8.8 (orig.)
assignment*
Examples 8.12, 8.13 (orig.)
Exercises 8.4, 8.14, 8.15, 8.19,
8.20, 8.22 (orig.)
Chapter 8 exercises
Finite fields
Ch. 9.1 – 9.2
Error detecting codes
Ch. 9.3
Error correcting codes
Ch. 9.4
More error correction
Ch. 9.5
Examples 9.6, 9.7, 9.8, 9.9
Exercises 9.3, 9.4, 9.5, 9.7
Shannon’s noisy channel
theorem
Ch. 9.6 – 9.7
Example 9.10, 9.11, 9.12
Exercise 9.8, 9.9
Secret codes – Fermat’s
theorem
Ch. 10.1
An encryption technique
Ch. 10.2
Examples 9.1, 9.2
Examples 9.4, 9.5
Examples 10.1, 10.2
Example 10.3
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Examples 10.4, 10.5, 10.6
Euclid’s algorithm
Ch. 10.3
Computer example
Ch. 10.4
Public key encryption –
Euler’s theorem
Ch. 10.5
Quantum cryptography –
axioms
Ch. 11.1
Dirac notation
Ch. 11.2
Quantum encryption
Ch. 11.3
Examples 10.7, 10.8
Examples 11.1, 11.2, 11.3, 11.4,
11.5
Examples 11.6, 11.7
Examples 11.8, 11.9, 11.10
Exercises 11.2, 11.3, 11.4, 11.5
Chapter 11 exercises
Synergy and information –
Shannon
Ch. 12.1
Synergy and information quantum
Ch. 12.2
Single product production
Ch. 12.3
Entanglement
Ch. 12.4
Synergy and multiple product
production
Ch. 12.5
Measurement implications
Ch. 12.6
Example 12.1
Example 12.2
Exercises 12.1, 12.2, 12.3, 12.10,
12.16
Chapter 12 exercises
Example 13.1
Arbitrage free pricing
(review)*
Ch. 13.1
Equilibrium conditions*
Ch. 13.2
Eigenvalues*
Ch. 13.3
Example 13.3
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Example 13.1 (cont.)
Transition probabilities using
eigenvalues*
Ch. 13.4
Unconditional probabilities –
Ross recovery theorem*
Ch. 13.5
Example 13.1 (cont.)
Exercises 13.1, 13.2, 13.3, 13.4,
13.5
Ch. 13 exercises*
Bayes normal revision
Ch. 7.1 - 7.2
Accounting set-up
Ch. 7.3
Information stocks and flows
Ch. 7.4
Accounting stocks and flows
Ch. 7.5
Examples 7.1, 7.2
Exercise 7.6
Examples 7.3, 7.4
Examples 7.3, 7.4
Exercise 7.4
Items with asterisk (*) might be omitted or de-emphasized depending on time and
interest.
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