It should be time to study and apply a mathematical accounting model which is easy to understand and audit, and is accurate and reliable. The paper distinctly describes three accounting's concepts or models (physical accounting model, double-entry system model, and mathematical accounting model) and their relationships. The physical accounting model naturally exists since business emerging and is the base of all other accounting models. The physical accounting model is actually consisted of every transaction which is based on a principle: exchange of equal values. The double-entry system model, which is still used all over the world, uses a logical method to keep recording transactions accurate. Its main characters are the T account with debit and credit, chart of accounts, two classes of permanent and temporary accounts, and trial balance. The mathematical accounting model is based on a basic expanding accounting equation and has developed following main characters: mathematical axiom principle, dynamic accounting equation, sub-equation of the dynamic accounting equation, five classes of permanent accounts, multi-subaccount name, structures of financial statements, and account flow statement. The same parts of the double-entry system and mathematical accounting models are to satisfy the basic accounting equation at the beginning of a fiscal year and the ending of a fiscal year, but the difference of them is that they take the different ways to reach the ending of the fiscal year. Based on the mathematical accounting model, I have developed a MathAccounting software. The MathAccounting software, which will be introduced in detail, has four function models: Transactions, Reports, Backup/Restore, and Maintenances. The MathAccounting software has little limitation, so it can be used by all economic entities regardless of their size, nature of business, and form of business organization without any altering. The paper also introduces a concept of the great accounting, which is based on the MathAccounting software and the wealth conservation law, in detail. The great accounting means two aspects. In the great data time, centered management of accounting is an inexorable trend. Every business company can login in a government's centered database by using of its business number. And every department in an organization can do part work of the accounting about itself duty. All works of the organization's departments will be made up of the financial statements. The great accounting has many advantages, such as being difficult to draw up false accounts and to evade a tax.
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