A Transition to Advanced Mathematics. Mathematics and Computer Sciences Department. o Work Experience, General. o Open Entry/Exit

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1 SECTION A - Curse Infrmatin 1. Curse ID: 2. Curse Title: 3. Divisin: 4. Department: MATH 245 A Transitin t Advanced Mathematics Natural Sciences Divisin Mathematics and Cmputer Sciences Department 5. Subject: 6. Shrt Curse Title: 7. Effective Term:: Trans. t Advanced Math Summer 2006 SECTION B - Official Curse Infrmatin 1. Recmmended Class Size: a. Maximum Class Size: 36 b. Class Size Apprval Date: 2. Methd f Instructin: þ Lecture Labratry Lecture and Labratry Wrk Experience, Occupatinal Wrk Experience, General Open Entry/Exit Independent Studies Distance Learning (Distance Educatin Delayed) fr nline curses. Distance (Hybrid Online) fr nline supprted curses 3. Cntact Hurs fr a Term: Nte: If nt a variable unit/hur curse, enter the hurs in the "Lw" clumn nly. Leave the hurs in the "High" clumn blank. Lw High Lecture: T Lab: T Lab/Lecture Parity? Yes N Activity: T Clinical: T Ttal Hurs 54 T 4. Credit Units: 3.00 T 1 Unit f credit per eighteen (18) hurs f lecture cntact hurs fr a term 1 Unit f credit per fifty-fur (54) hurs f lab, activity r clinical cntact hurs fr a term 5. Taxnmy f Prgrams (TOPS) Infrmatin: a. TOPS Cde and Curse Prgram Title: Page 1 f 5

2 Mathematics, General b. Curse Cntrl Number: (T be entered by the Instructin Office Only.) 6. SAM Pririty Cde:(Select One) Apprenticeship Curses ffered t apprentices nly. Advanced Occupatinal Curses taken in the advanced stages f an ccupatinal prgram. Each B level curse must have a C level prerequisite in the same prgram area. Clearly Occupatinal Curses taken in the middle stages f an ccupatinal prgram. Shuld prvide the student with entry-level jb skills. Pssibly Occupatinal Curses taken in the beginning stages f an ccupatinal prgram. þ Nn-Occupatinal 7. Please place this curse int the apprpriate discipline by selecting frm the drp dwn list. The discipline placement indicates what preparatin is needed t teach the curse. Discipline faculty may place their curses int mre than ne discipline as apprpriate: 8. General Curse Infrmatin a. Curse Credit Status: b. State Transfer Cde: c. State Classificatin Cde: d. Basic Skills Status/Level: e. Sprts/Physical Educatin Curse: A Transferable, UC/CSU/Private A Liberal Arts/Sciences Degrees N Nt a Basic Skills Curse Yes ( Only check here if the curse is a physical educatin curse.) f. Grading Methd: g. Number f repeats allwed: Letter Grade Only Nn-repeatable Credit (equates t 0 repeats) h. Overlap/Duplicate Curse: 9. Curse Preparatin: Nte: If this curse has a new requisite, a cntent review supplemental frm must be cmpleted. þ Prerequisite MATH 181 Page 2 f 5

3 Crequisite Advisry Nne 10. Curse Special Designatrs 11. Curse Prgram Status þ Prgram Applicable Stand-alne 12. Funding Agency Categry: þ Nt Applicable Primarily develped using ecnmic develpment funds Partially develped using ecnmic develpment funds SECTION C - Transfer Status Baccalaureate Status is granted by the Educatinal Design General Educatin and Baccalaureate Level Subcmmittee. þ CSU Transferable Apprval Date: þ UC Transferable SECTION D - General Educatin Request Mt. San Antni Cllege and CSU General Educatin curse apprval are submitted t the Educatinal Design GE and BL Subcmmittee fr apprval. 1. The Articulatin Officer submits the curse directly t the CSU Chancellr fr apprval. 2. Upn receiving apprval, the curse is apprved fr the Mt. SAC Assciate Degree GE and placed in the area(s) CSU apprval indicate(s). Yes þ N Apprved fr inclusin n Mt. SAC and CSU General Educatin List? 1. Mt SAC General Educatin Applicability: 2. CSU General Educatin Applicability (Requires CSU apprval): 3. IGETC Applicability (Requires CSU/UC apprval): Page 3 f 5

4 SECTION E - Curse Cntent 1. Curse Descriptins a. Catalg Descriptin A transitin t the rigrs f upper-divisin mathematics curses. Basic set thery and lgic, relatins, functins, mathematical inductin, the well-rdering principle, cuntable and uncuntable sets, the Schrder-Bernstein Therem, the axim f chice, Zrn's Lemma, the Heine-Brel Therem, the Blzan-Weierstrass Therem. Special emphasis n hw t present and understand mathematical prfs. b. Class Schedule Descriptin: þ Yes N Is a curse descriptin t be printed in the Class Schedule? A transitin t the rigrs f upper-divisin mathematics curses. Emphasis n hw t present and understand mathematical prfs. 2. Curse Outline Infrmatin a. Lecture Tpical Outline: - Prpsitins and cnnectives, cnditinals and bicnditinals, quantifiers, mathematical prfs, prfs invlving quantifiers - Ntatins f set thery, set peratins, DeMrgan's Laws, inductin - Cartesian Prduct, relatins, equivalence relatins, partitins - Functins, nt functins, ne-t-ne functins, induced set functins - Equivalent sets, finite sets, cuntable sets, uncuntable sets, Schrder-Bernstein Therem, the Axim f Chice, Zrn's Lemma - Prperties f real numbers, cmpleteness f real numbers, the Heine-Brel Therem, the Blzan-Weierstrass Therem - Final exam b. Lab Tpical Outline: 3. Curse Measurable Objectives: 1. Use techniques such as cntradictin and cntrapsitive t prve statements. 2. Perfrm set peratins using unin, intersectin, cmplementatin, and DeMrgan's Laws. 3. Write prfs invlving the well-rdering principle and mathematical inductin. 4. Write prfs pertaining t relatins, equivalence relatins, partitins, and equivalence classes. 5. Write prfs invlving ne-t-ne functins, nt functins, preimage, and inverse image. 6. Write prfs pertaining t finite sets, cuntable sets, and uncuntable sets. Apply the Bernstein-Schrder Therem t prve the equivalence between sets. 7. Use the Axim f Chice t prve statements pertaining t the cardinality f a set. Apply the Axim f Chice t prve the Cmparability Therem. 8. Use the Heine-Brel Therem t prve statements invlving cmpact sets. 9. Use the Blzan-Weierstrass Therem t prve statements invlving accumulatin pints and limit pints. 4. Curse Methds f Evaluatin: Categry 1. Substantial written assignments fr this curse include: If the curse is degree applicable, substantial written assignments in this curse are inapprpriate because: The curse primarily invlves skills demnstratins r prblem-slving Page 4 f 5

5 Categry 2. Cmputatinal r nn-cmputatinal prblem slving demnstratins: Exams Hmewrk prblems Quizzes Categry 3. Skills Demnstratins: Class perfrmance Perfrmance exams Categry 4. Objective Examinatins: Crrectness f calculatins and prfs 5. Sample Assignments: 1. Prve that every infinite set has a denumerable subset. 2. Prve that if a bunded subset f the real numbers has n accumulatin pints, the set is finite. 3. Let R be an equivalence relatin. Shw xry if x/r = y/r. 4. Use the well-rdering principle t prve the mathematical inductin. 6. Representative Text: Bk 1: Authr: Title: Publisher: Date f Publicatin: Editin: Smith, Dug; Maurice Eggen; A Transitin and Richard t St. Advanced Thmsn Andre. Brks/Cle Mathematics th Editin Page 5 f 5