AMIS H4780 Honors accounting and linear algebra
Spring 2014
2:20-3:40 TR
210 Gerlach
Professor Doug Schroeder
Office: Fisher 424
10:00-11:00 MW
schroeder_9@fisher.osu.edu
phone: 292-6427
Description: Honors accounting and linear algebra is a foundations building course for
the accounting honors program. Accounting structure is modeled as a linear system
composed of four fundamental subspaces: rowspace, columnspace, nullspace, and left
nullspace. Efficient information system design draws on nonlinear and/or linear
optimization. Consistent information analysis is predicated on probability theory (Bayes
theorem). Accounting accruals are statistics whose properties merit study. If time permits
we’ll expand our exploration beyond classical information to include quantum
information whose ideas are fundamental to the study of data security including quantum
encryption and perhaps the future of information science generally.
Objectives: The course aims to build strong foundations for the study of accounting as an
information science. Linear and nonlinear modeling are valuable tools for disciplining
and deepening our understanding of accounting; in other words, the pursuit of accounting
information science.
Textual materials: Notes and example problems are posted on the course web page.
Recommended but optional texts include
Christensen and Demski (CD), Accounting Theory: An Information Content Perspective,
McGraw-Hill Irwin, 2003.
Demski (D), Managerial Uses of Accounting Information, Springer, 2008.
Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 2009.
Classroom approach: Students are expected to actively engage in discussion of topics
with an emphasis on recognizing the intersection of the various topics. That is, we will
attempt to reinforce commonalities across topics and not start from scratch with each
topic. Each session tests our understanding and active participation is expected.
The course concludes with a final written exam during the university exam period.
Evaluation:
Classroom participation, positive contribution to learning environment,
quizzes, homework
Final exam
80%
20%
tentative outline:
Session
Topic
1
Introduction – A matrix, network
graph, aggregate accounts
2
Introduction – optimization
3
6
Introduction – one of many sources of
information
Introduction – information (decision)
analysis
Linear systems of equations –
fundamental theorem of linear
algebra; matrix operations (addition,
multiplication, vector inner & outer
products, transposition)
Identities & inverse operations
7
Triangularization – LU factorization
8
Diagonalization – eigenvalues &
eigenvectors
Diagonalization – Cholesky &
spectral decomposition
Singular value decomposition &
pseudo-inverse and QR decomposition
Optimization – linear regression &
projections
4
5
9-10
11-12
13-14
15-16
17
Optimization – linear regression,
projections & conditional
expectations, GLS & Cholesky
decomposition
Optimization – Lagrangian, KarushKuhn-Tucker conditions
18
Unconstrained optimization
19
Optimization – fundamental theorem
of linear programming, duality
theorems
Optimization – duality & theorem of
the separating hyperplane
(fundamental theorem of finance)
20-21
Assignment
Ralph’s structure
Ralph’s probability assignment
ch. 4, appendix H.2
Ralph’s information partition (part A)
CD ch. 5, D ch. 9
Ralph’s fineness
CD ch. 5, D ch. 9
Ralph’s subspaces
appendix A.2
Ralph’s inverse
appendix A.3
Ralph’s decomposition
appendix A.3, A.4
Ralph’s equilibrium
appendix A.4
Ralph’s symmetry
appendix A.4
Ralph’s row component
appendix A.4
Ralph’s estimate;
Ralph’s optimal accruals
ch. 2, appendix D.1
Ralph’s double residual regression;
Ralph’s GLS
ch. 2.7, appendix D.2
Ralph’s binomial probability
assignment
Ralph’s density assignment
ch. 4, appendix H.2
Ralph’s discrete choice
appendix G, notes on random utility
model
Ralph’s bounds;
D ch. 8, appendix A.1, H.1
Ralph’s aggregate accounts;
Ralph’s derivatives
appendix H.3
Session
22
Topic
Classical information analysis – stateact-outcome (utility)
Assignment
Ralph’s decision
CD ch. 5
23-24
Classical information analysis – Bayes
theorem (sum & product rules, law of
total probability, iterated expectations,
variance decomposition)
Classical information analysis – Bayes
normal
Ralph’s information partition (part B);
Bayesian Ralph
appendix B, C
25-26
27
28
29
30
31
Quantum information – vector spaces;
superposition, transformation,
combination & measurement
Quantum information – Bell’s
inequality & quantum entanglement
Quantum information – unitary
operators & measurement
Quantum information – observables &
measurement
Quantum information – quantum
entanglement
Final exam
W 4/23
2:00-3:45
Normal Ralph;
Ralph’s accounting information
appendix C
Ralph’s teleportation
appendix I
Ralph’s inequality
appendix I
Ralph’s synergy (part A)
appendix I
Ralph’s synergy (part B)
appendix I
Ralph’s synergy (part C)
appendix I