Martina Bode | University of Illinois at Chicago (original) (raw)
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− → O X where d(f 1 ∧ f 2 ∧ ... ∧ f k) = Σ 0≤i≤k (−1) i Ψ(f i)f 1 ∧ ... ∧ f i ∧ ... ∧ f k. This i... more − → O X where d(f 1 ∧ f 2 ∧ ... ∧ f k) = Σ 0≤i≤k (−1) i Ψ(f i)f 1 ∧ ... ∧ f i ∧ ... ∧ f k. This is a well defined complex. Lemma 1.2. Suppose that the image of Ψ is equal to the ideal sheaf I Y of a locally complete intersection Y ⊂ X. Further more if rank(F) = codim X Y , then the Koszul complex K(F , Ψ) is exact. Proof. This is just a local question, therefore choose an open cover U = {U i } of X, such that for all open sets U
EDULEARN proceedings, Jul 1, 2022
Notices of the American Mathematical Society, 2009
Clickers (electronic voting systems) are all the buzz in higher education these days as many univ... more Clickers (electronic voting systems) are all the buzz in higher education these days as many universities and colleges invest significant sums of money to integrate these systems into their classrooms. But what are clickers? Are they just another high-tech gimmick, or can they really be used to improve learning? Can clickers be used efficiently in calculus classes? In an ideal world, students would take calculus for the sheer love of it. The reality is, however, that calculus is a service course, and most students take it to fulfill university requirements. Engaging students in calculus classes thus can be a challenge. Furthermore, in traditional lectures, students passively take notes, at times barely processing the material as they struggle to keep their attention focused for an hour. Students often fear that they are alone in not understanding the material and are at times afraid of asking questions in class. At the end of class, both students and instructor may leave without kno...
EDULEARN19 Proceedings, 2019
In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grass... more In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.
The most recent (2004) data from the U.S. Department of Education states that many students enter... more The most recent (2004) data from the U.S. Department of Education states that many students entering a college calculus course have taken calculus in high school, the majority in Advanced Placement (AP) courses. Therefore, students enrolling in college calculus courses have a wide range of background preparation, from weak precalculus to AP credit that allows them to place into calculus II or III. In this document, we consider the transition of students from AP courses to college calculus. There are a number of studies that suggest that AP classes prepare students well for college classes, especially those students who place into calculus II and calculus III [1, 2, 3]. However, students who do not take the AP exam, or whose high school calculus is weak, may have difficulty in their college calculus course. Therefore, we focus here on students making the transition from high school AP calculus classes to calculus I in college, as opposed to students starting in collegiate calculus II...
In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grass... more In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.
Notices of the American …, 2009
Clickers (electronic voting systems) are all the buzz in higher education these days as many univ... more Clickers (electronic voting systems) are all the buzz in higher education these days as many universities and colleges invest significant sums of money to integrate these systems into their classrooms. But what are clickers? Are they just another high-tech gimmick, or can they ...
− → O X where d(f 1 ∧ f 2 ∧ ... ∧ f k) = Σ 0≤i≤k (−1) i Ψ(f i)f 1 ∧ ... ∧ f i ∧ ... ∧ f k. This i... more − → O X where d(f 1 ∧ f 2 ∧ ... ∧ f k) = Σ 0≤i≤k (−1) i Ψ(f i)f 1 ∧ ... ∧ f i ∧ ... ∧ f k. This is a well defined complex. Lemma 1.2. Suppose that the image of Ψ is equal to the ideal sheaf I Y of a locally complete intersection Y ⊂ X. Further more if rank(F) = codim X Y , then the Koszul complex K(F , Ψ) is exact. Proof. This is just a local question, therefore choose an open cover U = {U i } of X, such that for all open sets U
EDULEARN proceedings, Jul 1, 2022
Notices of the American Mathematical Society, 2009
Clickers (electronic voting systems) are all the buzz in higher education these days as many univ... more Clickers (electronic voting systems) are all the buzz in higher education these days as many universities and colleges invest significant sums of money to integrate these systems into their classrooms. But what are clickers? Are they just another high-tech gimmick, or can they really be used to improve learning? Can clickers be used efficiently in calculus classes? In an ideal world, students would take calculus for the sheer love of it. The reality is, however, that calculus is a service course, and most students take it to fulfill university requirements. Engaging students in calculus classes thus can be a challenge. Furthermore, in traditional lectures, students passively take notes, at times barely processing the material as they struggle to keep their attention focused for an hour. Students often fear that they are alone in not understanding the material and are at times afraid of asking questions in class. At the end of class, both students and instructor may leave without kno...
EDULEARN19 Proceedings, 2019
In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grass... more In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.
The most recent (2004) data from the U.S. Department of Education states that many students enter... more The most recent (2004) data from the U.S. Department of Education states that many students entering a college calculus course have taken calculus in high school, the majority in Advanced Placement (AP) courses. Therefore, students enrolling in college calculus courses have a wide range of background preparation, from weak precalculus to AP credit that allows them to place into calculus II or III. In this document, we consider the transition of students from AP courses to college calculus. There are a number of studies that suggest that AP classes prepare students well for college classes, especially those students who place into calculus II and calculus III [1, 2, 3]. However, students who do not take the AP exam, or whose high school calculus is weak, may have difficulty in their college calculus course. Therefore, we focus here on students making the transition from high school AP calculus classes to calculus I in college, as opposed to students starting in collegiate calculus II...
In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grass... more In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.
Notices of the American …, 2009
Clickers (electronic voting systems) are all the buzz in higher education these days as many univ... more Clickers (electronic voting systems) are all the buzz in higher education these days as many universities and colleges invest significant sums of money to integrate these systems into their classrooms. But what are clickers? Are they just another high-tech gimmick, or can they ...