[PDF] Superrigidity of Hyperbolic Buildings

Mathematics Department Stanford University Math 61CM/DM

Math 61CM/DM { Basic algebraic structures The purpose of this handout is to provide some basic de nitions and a brief discussion of some key ideas and objects in algebra One main new idea you will be studying in class is the notion of a eld This is a concept which generalizes the algebraic properties of the real numbers

CCSS Alignments for Dimensions Math® 6—8

CCSS Alignments for Dimensions Math® 6—8 Singapore Math Inc www singaporemath com CCS: Common Core Standards DM: Dimensions Math 6—8 Ratios & Proportional Relationships Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane

Mathematics Department Stanford University Math 61CM/DM

Math 61CM/DM { Inner products Recall the de nition of an inner product space; see Appendix A 8 of the textbook De nition 1 An inner product space V is a vector space over R with a map h;i: V V R such that 1 (Positive de niteness) hx;xi 0 for all x2V, with hx;xi= 0 if and only if x= 0 2

Superrigidity of Hyperbolic Buildings

As explained in [DM] T P Y is an unbounded F-connected euclidean cell complex obtained by taking the tangent spaces to all the DM’s passing through P with the appropriate identifications Furthermore, the exponential map expY P: B r(0) ⊂ T Y → B(P) ⊂ Y is defined by piecing together the exponential maps of all the DM’s containing P

Dimensions Math Placement Test 2B

This test covers material taught in Dimensions Math 2B 1 Add using mental math (a) (b) (c) (d) 2 Find the missing number (e) (f) 36 + 40 = 50 + 375 = 32 + 199 =

Fall 2013, Course 18769: Algebraic D-modules TR 11-1230, Rm

INSTRUCTIONS ON SWITCHING FROM MATH 61 TO MATH 51

INSTRUCTIONS ON SWITCHING FROM MATH 61 TO MATH 51 The Math department has a process for you to transfer from Math 61CM/DM to Math 51, should you decide to do so, up to 6 days after the rst 61CM/DM midterm exam The procedure is explained below, broken into cases depending on when you choose to make the trasnfer

Fundamentals of Mathematics I

Examples: Decimals on the Number Line Example 5 a) Plot 0 2 on the number line with a black dot b) Plot 0 43 with a green dot Solution: For 0 2 we split the segment from 0 to 1 on the number line into ten equal pieces between 0 and 1 and then count

Chapter Four: The Mathematics of Apportionment

Math Course Enrollment (p i) Standard Quota (q i) Lower Quota (LQ) Rank Sections Math A 400 st10 929 10 1 11 Math B 90 2 459 2 2 Math C 225 6 148 6 6 Math D 200 5 464 5 2nd 6 Total Enrollment (P) 915 Initial Apportionment 23 Final Apportionment 25 Total Sections (M) 25 Standard Divisor (SD)