Show that if p is an odd prime and a is an integer not divisible by p. then the congruence x2 ≡ a (mod p) has either no solutions or exactly two incongruent solutions modulo p.
Day 1 - Mills -> Sociological Imagination -> developing quality of mind -> bridging history & biography - What we think might be personal troubles might be impacted by public issues o Unemployment 1 person in a city vs. half of city unemployed - Public issue person may not be aware of can still impact them o External vs. internal factors - War -> Boeing o Tech. changes, competition, relocation o Fewer jobs for WA people -> public issue o More people go to college in order to get a job & take care of family o History impacting biographies - Things that happen to you -> not always your fault - Quality of mind -> thinking beyond self o May make best decision for you and family o Better analysis of the situation - Berger -> Invitation to Sociology - “The first tenet of sociology is this: things are not what they seem.” - Ex: Conflict Theory -> describes things as they are* o Haves/Have-nots (hierarchy) ->individual choices place people in this hierarchy o Mostly resonates in the U.S. o *Structure = static – like a building o Student/teacher -> assume students who do well choose to do well -> doesn’t allow us to ask a lot of questions Maybe they learn differently Grades reflect teaching, teaching reflects labor -> relational If they’re integrated, dif. Structure Educational vs. schooling o Freedom, individual choices, responsibility, equal opportunity, rights - Ontology -> atomistic, individualistic, mechanistic VS. - Relational – Marx - Structure -> can change (doesn’t have to be for the better) - Freedom -> knowing that things are not static & can change o Rules of the system (“game”) that impact H/HN - Wealth in Conflict Theory language -> H/HN, top 1% vs. 99% o Tell 1% to give 99% opportunity -> opportunity for what - Don’t talk about the rules & system o Limits our thinking - Back to labor controlling capitalists & laborers in different ways - Step back & look at it from a different angle o Gives possibility to think of different things Help H/HN simultaneously o Gap between them doesn’t have to be as big but in the capitalist system there has to be H/HN o Rules can change (i.e. baseball, football, etc.) Capitalist system in 1800s different than now b/c of this o Keynesian Capitalism -> Democratic Socialism (U.S.) Social Security, Medicare, Medicaid, Family Leave Act, min. wage o Basque – Spain -> distributism - Too much of a gap -> crazy stuff happens - “Things are not what they seem” o Ask different questions o Think structure is static but it’s no - Other animals born into structures already there o Humans created our own Doesn’t make sense to think we can’t change it - System currently allows 1& to gain more & more o Not helping 99% as much o 1% isn’t the villain necessarily o change system so there isn’t as much of a gap as long as we’re capitalists, still going to be a difference - Marx p. 33 paragraph 3 “We must bear in mind… that man’s relation to himself becomes for him objective and actual through his relation to the oter man.” - How do you know you’re a student o Student loans o Enrolled in a program/class o Homework & tests for the class o Stress for high GPA o Rules, norms, values associated w/ students - You become the student when you adhere to the behaviors associated w/ being a student o In relation to the other & structure itself - Don’t just individually create selves - Compare & contrast - Different places in society - Often in relation to something else Day 2 - Aronowitz - Against Schooling o Education -> enjoyable & applicable for the rest of your life - Social class & inequality o If you come from a certain worldview it will lead you down a path -> how your biography is impacted by history - Berger – Sacred Canopy (Processes of worldbuilding fundamental dialectic society) 1. Externalization 2. Objectivation 3. Internalization o Related processes - Everyone has internalized this worldview of liberalism -> our solutions tto problems reflect this - Different understandings of things -> what’s normal, abnormal, etc. o Created o How do they impact us - Externalization o “Ongoing physical & mental activity of man in the world…” (part of it) o Create things o Usefulness of fire o Man creates society (and everything in it) - Objectivation o Conversion of a concept to an object o Fire Cooking Keeping warmth o Go back to externalization of matches, lighter/lighter fluid, etc. o Making reality happen o Vessel to show usefulness of what you created - Social interaction - Recognition of the need - Show what to do/what not to do - Prove thing is useful, create a need - Create norms, rules, etc. - Internalization o Know it in your head, become conscious of it o Become habitual -> don’t have to think about it anymore o Through process of socialization we internalize Family Peers Various institutions Media - Social construction of reality - Didn’t become useful until we made it useful o Fire, water Out there, not created by man, but man created a usefulness for it Converted concept of usefulness to it After a while, habitual Externalize other things for it - Society doesn’t develop linearly o Take steps backward, rethink things, move forward o Some things have constant progression - How does change occur o Not all things have to change o Not necessary to go from one point to another or constantly move forward o Reliant on us o Institute change Externalize different use or different way - See something interesting, find use for it, show it to other people, become a norm - In order to show the usefulness of something, have to show it in relation to something else - Concepts can stay the same -> uses and vessels may change Day 3 (Video – Race: The Power of an Illusion, vol. 2: The Story We Tell) - Race is an idea o Constructed by society to further political and economic goals - Thomas Jefferson o “Blacks are inferior to whites” o Articulates theory of race o Wrote “all men are created equal” in the Declaration of Independence Yet he owned 200+ slaves Freedom only applies to certain people Get away w/ excluding them by saying there’s something different about them “Not quite men” “Out of the human family” - Used to be distinguished by religion & wealth o Status instead of black & white - Turned to Trans Atlantic slave trade o Replaced indentured servants w/ slaves - “Christian” replaced w/ “white” - “Ego enhancement” & status white people got from racism - Slavery identified w/ Africans o People began to see it as natural - American Indians o TJ saw them as not much different from Europeans o “Naturally white people, just looked different because of sun exposure” o Savages but could be civilized o Other settlers thought they should be driven out o Cheapest/easiest way to avoid war & to acquire land “Civilize” them Assimilation Education, convert from hunters to farmers Assimilation of black people not supported - Try to call on science to figure out what makes blacks different from whites - Louisiana Purchase o American Indians lived there already - Cherokees transform, on a superficial level, their culture o Treaties ceding 90% of their land to U.S. o Some owned slaves, farmers, Christian, bilingual newspapers, gov’t patterned after U.S. - Taking American Indian lands and giving it to whites - Andrew Jackson 1828 o “Common Man” a.k.a. white men o Removing all American Indians east of the Mississippi is main goal Indian Removal Act Trail of Tears Forced out, relocated, ¼ died - American Indians first told to abandon I.D. o Now told it’s inherent & should be embraced o In other words, they are no longer white people - Manifest Destiny & western expansion o Idea that the West belonged to white Americans - Momentum towards abolition of slavery o Tension builds o Debate over slavery, race, status of blacks o Question over species (are all people of different races the same species) o Trying to use science to back it up Skull size -> brain capacity Systematic errors in favor of systematic hierarchy o Race as defense of slavery Belief of different species, “created as inferior” o Belief it didn’t violate democracy b/c “all men” didn’t apply to black people - Types of Mankind o First time races are distinctly separated & listed - Dred Scott Decision o Enslaved or free could never become citizens - War -> Emancipation Proclamation - When slavery is over -> rationalization for it remains o Would have been different if the justification was “we need their labor & we have the power to do this” - “White Man’s Burden” - World’s Fair o Tech. & cultural exhibits o Also human exhibits in “natural habitats” Exploitation -> show them as defeated or conquered Geronimo signing autographs Recreation of plantation life o “Highway of human progress” “Who’s in the fast lane” Hint: it’s white people