Mount Saint Vincent University
BIOL 1153 Introductory Biology II
Dr. Jessica Boyd
Quiz I Study Guide
Chapter
Section
Pages
26 Origin of Life
26.1 Deep Time
26.2 Origins of Life
26.3 Evidence for Early Life
26.4 Earths Changing System
26.5 Ever- Changing L
Mount Saint Vincent University
BIOL 1153 Introductory Biology II
Quiz IV Study Guide
Dr. Jessica Boyd
Quiz Date April 3, 2017
Chapter
Section
Page
42 Animal Body
and Principles
of Regulation
42.1 Organization of the Vertebrate Body
42.2 Epithelial Tissue
Mount Saint Vincent University
BIOL 1153 Introductory Biology II
Dr. Jessica Boyd
Quiz II Study Guide
Chapter
Section
29 Protists
29.1 Eukaryotic Origins and Endosymbiosis
29.2 Overview of Protists
29.3 Feeding Groove in Excavata
29.4 Secondary Endosymbio
Questions Lab 6 Bryophytes
1. How are spores released from the cap?
The plant creates pressure inside the cap and an explosion of spores in the air the wind helps it
blow away from the parent plant.
2. Which stage of the mosses is the largest? (gametophyt
Lab 5 questions
1. How does the number of chloroplasts in Euglena compare with that found in Chlamydomonas?
In Euglena, tiny sacs of chloroplast are numerous throughout the cell. In the Chlamydomonas it has one
single large cup shape that takes up almost
Lab 3
Questions:
8. I think the importance of evolution of the vascular cambium is allows the plant to get wider in size.
9. the function of the vascular cambium is the vascular system of the plant. The primary xylem in the
vascular cambium carries water
Lab 4
Questions
1. The taproot root system has one large root with many branches of roots that comes off of it. The
taproot can penetrate deeper in the earth and is only in dicot plants. While the fibrous root
system has a many finer roots with no main la
Lab 7 Ferns
Questions
1. What is the function of the rhizome and rhizoids?
The rhizome is stems that is partially underground that help support the plant. The rhizoid is hair like
projects that helps the plant absorb water and nutrients by increasing the
General Ecology Lab Manual
1
Lab 9: Plant Competition
Due: November 24, 2016
Name: Helen Wong
INTRASPECIFIC PLANT COMPETITION
Procedure 9.1: Examine competition among sunflower seedlings
1. Count and record in table 9.1 the number of plants surviving. The
Lab 8: Species Diversity
Due: Nov 17th, 2016
Name: Helen Wong
Questions 1
In your experience, which is more common, a community dominated by a few species, or a
community with all species equally?
A community dominated by a few species.
Species richness m
BIOL 3312 Ecology Lab
October 20, 2016
Lab 6: Micro-Community Assessments
Due: Nov 3, 2016
Name: Helen Wong
Procedure 6.1: Sample a lichen micro-community
1. Determine the area of each lichen.
a. Outline each lichen on graph paper with lines marking four
BIOL 3312 General Ecology Lab
Lab 4: Terrestrial Plant and Community Assessment
Due: Oct 13, 2016
Name: Helen Wong
Procedure 4.1: Observe and assess the ecological characteristics of a terrestrial
community
1.
How might shade affect the temperature of the
94
2. Discrete Logarithms and DieHellman
(b) R = Z, = multiplication, and addition is as usual. The multiplicative
identity element is 1. The only elements that have multiplicative inverses
are 1 and 1, so Z is a ring, but it is not a field.
(c) R = Z/nZ,
90
2. Discrete Logarithms and DieHellman
is a discrete logarithm problem whose base is an element of order q. By assumption, we can solve this problem in Sq steps. Once this is done, we know
an exponent x0 with the property that
g x0 q
e1
= hq
e1
in G.
We
98
2. Discrete Logarithms and DieHellman
We can now define common divisors and greatest common divisors in F[x].
Definition. A common divisor of two elements a, b F[x] is an element d
F[x] that divides both a and b. We say that d is a greatest common div
128
3. Integer Factorization and RSA
getting a witness. Since Bob found no witnesses in 10 tries, it is reasonable2
to conclude that the probability of n being composite is at most (25%)10 ,
which is approximately 106 . And if this is not good enough, Bob
158
3. Integer Factorization and RSA
In order to sieve p from F (t), we subtract an integer approximation of log p
from the integer approximation to log F (t), since by the rule of logarithms,
log F (t) log p = log
F (t)
.
p
If we were to use exact values
132
3. Integer Factorization and RSA
Bob finishes
his task. Notice that the running time of this naive algorithm
is O( n), so it is an exponential-time algorithm according to the definition
in Section 2.6
It would be nice if we could use the MillerRabin t
134
3. Integer Factorization and RSA
The exponent k is not equal to 0, so it is quite unlikely that ak will be
congruent to 1 modulo q. Thus with very high probability, i.e., for most choices
of a, we find that
p divides aL 1
and
q does not divide aL 1.
B
110
Exercises
(c) Suppose that b is a square root of a modulo pn . Prove that for some choice of j,
the number b + jpn is a square root of a modulo pn+1 .
(d) Explain why (c) implies the following statement: If p is an odd prime and if a
has a square root
100
2. Discrete Logarithms and DieHellman
Proof. The existence of a factorization into irreducibles follows easily from the
fact that if a = bc, then deg a = deg b+deg c. (See Exercise 2.33.) The proof
that the factorization is unique is exactly the same
108
Exercises
(a) Let eG be the identity element of G, let eH be the identity element of H, and
let g G. Prove that
(eG ) = eH
and
(g 1 ) = (g)1 .
(b) Let G be a commutative group. Prove that the map : G G defined
by (g) = g 2 is a homomorphism. Give an e
114
3. Integer Factorization and RSA
power is not 1 modulo 15? A moments reflection shows that each of the
numbers 3, 5, 6, 9, 10, 12, 15 has a nontrivial factor in common with the modulus 15, while the numbers 1, 2, 4, 7, 8, 11, 13, 14 are relatively pri
118
3. Integer Factorization and RSA
17389d 1 (mod 63840),
where 63840 = (p 1)(q 1) = 228 280. The solution, using the method
described in Remark 1.15 or Exercise 1.12, is d 53509 (mod 63840). Then
Proposition 3.4 tells us that
x 4392753509 14458
(mod 643
96
2. Discrete Logarithms and DieHellman
Definition. Let R be a ring and let m R with m = 0. For any a R,
we write a for the set of all a R such that a a (mod m). The set a is
called the congruence class of a, and we denote the collection of all congruenc
142
3. Integer Factorization and RSA
and we are searching for integers u1 , u2 , . . . , ur such that
e11 u1 + e21 u2 + + er1 ur 0
e12 u1 + e22 u2 + + er2 ur 0
.
.
.
.
(mod 2),
(mod 2),
e1t u1 + e2t u2 + + ert ur 0
(mod 2).
(3.17)
You have undoubtedly rec