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Proposition 1.1. α1, . . . , αn forms a basis for V ∗ (called the dual basis). In particular, this shows that V and V ∗ are vector spaces of the same dimension. However, there is no natural way to choose an isomorphism between them, unless we pick some additional structure on V (such as a basis or a nondegenerate bilinear form). On the other hand, we can construct an isomorphism ψ from V to (V ...

Here are the notes I took for Wei Zhang’s course on modular forms offered at Columbia University in Spring 2013 (MATH G4657: Algebraic Number Theory). Hopefully these notes will appear in a more complete form during Fall 2014. I recommend that you visit my website from time to time for the most updated version. Due to my own lack of understanding of the materials, I have inevitably introduced b...

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Payroll Direct Deposit Form [1] Address Update [2] 2016 TD1 Federal Personal Tax Credit Return [3] 2016 Worksheet for Federal TD1 [4] 2016 TD1 Ontario Personal Tax Credit Return [5] 2016 Worksheet for Ontario TD1 [6] CPT30 [7] Election to Stop Contributing to the Canada Pension Plan Authorize RSP Payroll Deduction [8] Record of Employment (ROE) The University of Guelph submits all ROEs electron...

Differentials are an important topic in algebraic geometry, allowing the use of some classical geometric arguments in the context of varieties over any field. We will use them to define the genus of a curve, and to analyze the ramification of morphisms between curves. Although differentials remain important for arbitrary varieties, we will restrict our treatment to the case of nonsingular varie...

This paper presents work-in-progress on techniques for procedurally “growing” organic-looking forms. The goal is to design and implement techniques for expressing simple algorithmic operations that can be combined in various ways to produce forms that develop from an amorphous blob to a structured cellular assemblage. Growth “buds” in a cellular assemblage each execute short programs that deter...

Payroll Direct Deposit Form [1] Address Update [2] 2016 TD1 Federal Personal Tax Credit Return [3] 2016 Worksheet for Federal TD1 [4] 2016 TD1 Ontario Personal Tax Credit Return [5] 2016 Worksheet for Ontario TD1 [6] CPT30 [7] Election to Stop Contributing to the Canada Pension Plan Authorize RSP Payroll Deduction [8] Record of Employment (ROE) The University of Guelph submits all ROEs electron...