Lactose is the principal carbohydrate in the milks of all mammals; non mammalian sources are very rare. Milk contains only trace amounts of other sugars, including glucose(50 mg\), fructose, glucosamine, galac- tosamine, neuraminic acid and neutral and acidic oligosaccharides The concentration of lactose in milk varies widely between species(Table 2.1). The lactose content of cows'milk varies with the breed of cow

You may use one 8.5 11\sheet with notes in you own handwriting on both sides but no other sources of information Calculators are not allowed You may assume all results from lecture, the notes, problem sets, and recitation Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the probl

YOUR NAME Calculators are not allowed on this exam You may use one 8.5 x 11\sheet with notes in your own handwriting on both side but no other sources of information You may assume all results from lecture, the notes, problem sets, and recitation

1 Bipartite Graphs Graphs that are 2-colorable are important enough to merit a special name; they are called bipartite graphs. Suppose that G is bipartite. Then we can color every vertex in G ei ther black or white so that adjacent vertices get different colors. Then we can put all the

1 Coloring Graphs Each term, the MIT Schedules Office must assign a time slot for each final exam. This is not easy, because some students are taking several classes with finals, and a student can take only one test during a particular time slot. The Schedules Office wants to avoid all conflicts, but to make the exam period as short as possible

1 The Number-Picking Game Here is a game that you and I could play that reveals a strange property of expectation. 3, First, you think of a probability density function on the natural numbers. Your distri- bution can be absolutely anything you like. For example, you might choose a uniform distribution on 1, 2, ... 6, like the outcome of a fair die roll. Or you might choose a bi- probability, provided that,...,n. You can even give every natural number a non-zero nomial distribution on 0, 1 he sum of all probabilities is 1

All the questions are from Plummer, Chapter 10, p.679-680, which was handed out in class 1)Question 10.3 2) Question 10.4 3)Question 10.5 4) Question 10.6

What Is the Question of the Chapter? Suppose we observe a collection of a consumer's choices, can we discover his/her preference? Is this possible at all?fso, under what conditions is this possible? (This is the reverse question of finding the optimal choice)

Chapter 1 Separation processes-an overview A. S. GRANDISON and M. J. LEWIS Department of Food Science and Technology, The University of Reading, Whiteknights PO Box 226, Reading, RG6 6AP 1.1 FOODS- THE RAW MATERIAL Food and drink play a vital role in all our lives, providing us with the nutrients essential

All DNA is recombinant DNA. Genetic exchange works constantly to blend and rearrange chromosomes, most obviously during meiosis, when homologous chromosomes pair prior to the