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Preface |
7 |
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Acknowledgments |
8 |
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Contents |
9 |
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Part I: Beginnings |
15 |
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1 Dilemmas and Craftsmanship |
16 |
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1.1 Those Confounded Vitamins |
16 |
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1.2 Cochran’s Basic Advice |
17 |
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1.3 Maimonides’ Rule |
20 |
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1.4 Seat Belts in Car Crashes |
22 |
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1.5 Money for College |
23 |
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1.6 Nature’s ‘Natural Experiment’ |
24 |
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1.7 What This Book Is About |
26 |
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1.8 Further Reading |
31 |
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References |
31 |
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2 Causal Inference in Randomized Experiments |
34 |
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2.1 Two Versions of the National Supported Work Experiment |
34 |
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2.2 Treatment Effects in Randomized Experiments |
38 |
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2.3 Testing the Null Hypothesis of No Treatment Effect |
42 |
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2.4 Testing Other Hypotheses |
53 |
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2.5 Attributable Effects |
62 |
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2.6 Internal and External Validity |
69 |
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2.7 Summary |
70 |
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2.8 Further Reading |
70 |
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2.9 Appendix: Randomization Distribution of m-statistics |
71 |
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References |
74 |
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3 Two Simple Models for Observational Studies |
77 |
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3.1 The Population Before Matching |
77 |
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3.2 The Ideal Matching |
78 |
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3.3 A Na ¨ ive Model: People Who Look Comparable Are Comparable |
82 |
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3.4 Sensitivity Analysis: People Who Look Comparable May Differ |
88 |
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3.5 Welding Fumes and DNA Damage |
91 |
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3.6 Bias Due to Incomplete Matching |
97 |
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3.7 Summary |
98 |
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3.8 Further Reading |
99 |
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3.9 Appendix: Exact Computations for Sensitivity Analysis |
100 |
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References |
102 |
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4 Competing Theories Structure Design |
107 |
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4.1 How Stones Fall |
107 |
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4.2 The Permanent-Debt Hypothesis |
110 |
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4.3 Guns and Misdemeanors |
112 |
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4.4 The Dutch Famine of 1944–1945 |
112 |
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4.5 Replicating Effects and Biases |
113 |
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4.6 Reasons for Effects |
116 |
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4.7 The Drive for System |
120 |
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4.8 Further Reading |
121 |
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References |
122 |
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5 Opportunities, Devices, and Instruments |
125 |
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5.1 Opportunities |
125 |
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5.2 Devices |
128 |
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5.3 Instruments |
143 |
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5.4 Summary |
152 |
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5.5 Further Reading |
152 |
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References |
153 |
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6 Transparency |
158 |
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References |
160 |
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Part II: Matching |
161 |
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7 A Matched Observational Study |
162 |
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7.1 Is More Chemotherapy More Effective? |
162 |
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7.2 Matching for Observed Covariates |
163 |
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7.3 Outcomes in Matched Pairs |
166 |
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7.4 Summary |
168 |
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7.5 Further Reading |
170 |
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References |
170 |
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8 Basic Tools of Multivariate Matching |
171 |
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8.1 A Small Example |
171 |
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8.2 Propensity Score |
173 |
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8.3 Distance Matrices |
176 |
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8.4 Optimal Pair Matching |
180 |
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8.5 Optimal Matching with Multiple Controls |
183 |
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8.6 Optimal Full Matching |
187 |
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8.7 Efficiency |
191 |
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8.8 Summary |
192 |
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8.9 Further Reading |
192 |
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References |
193 |
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9 Various Practical Issues in Matching |
195 |
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9.1 Checking Covariate Balance |
195 |
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9.2 Almost Exact Matching |
198 |
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9.3 Exact Matching |
200 |
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9.4 Missing Covariate Values |
201 |
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9.5 Further Reading |
202 |
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References |
202 |
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10 Fine Balance |
204 |
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10.1 What Is Fine Balance? |
204 |
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10.2 Constructing an Exactly Balanced Control Group |
205 |
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10.3 Controlling Imbalance When Exact Balance Is Not Feasible |
208 |
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10.4 Fine Balance and Exact Matching |
210 |
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10.5 Further Reading |
211 |
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References |
211 |
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11 Matching Without Groups |
213 |
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11.1 Matching Without Groups: Nonbipartite Matching |
213 |
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11.2 Some Practical Aspects of Matching Without Groups |
217 |
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11.3 Matching with Doses and Two Control Groups |
219 |
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11.4 Further Reading |
226 |
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References |
226 |
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12 Risk-Set Matching |
228 |
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12.1 Does Cardiac Transplantation Prolong Life? |
228 |
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12.2 Risk-Set Matching in a Study of Surgery for Interstitial Cystitis |
229 |
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12.3 Maturity at Discharge from a Neonatal Intensive Care Unit |
233 |
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12.4 Joining a Gang at Age 14 |
236 |
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12.5 Some Theory |
237 |
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12.6 Further Reading |
238 |
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References |
239 |
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13 Matching in R |
241 |
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13.1 |
241 |
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13.2 Data |
242 |
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13.3 Propensity Score |
244 |
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13.4 Covariates with Missing Values |
244 |
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13.5 Distance Matrix |
246 |
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13.6 Constructing the Match |
247 |
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13.7 Checking Covariate Balance |
248 |
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13.8 College Outcomes |
250 |
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13.9 Further Reading |
251 |
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13.10 Appendix: A Brief Introduction to |
252 |
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13.11 Appendix: |
254 |
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Functions for Distance Matrices |
254 |
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References |
256 |
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Part III: Design Sensitivity |
258 |
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14 The Power of a Sensitivity Analysis and Its Limit |
259 |
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14.1 The Power of a Test in a Randomized Experiment |
259 |
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14.2 Power of a Sensitivity Analysis in an Observational Study |
267 |
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14.3 Design Sensitivity |
271 |
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14.4 Summary |
274 |
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14.5 Further Reading |
274 |
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Appendix: Technical Remarks and Proof of Proposition 14.1 |
274 |
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References |
276 |
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15 Heterogeneity and Causality |
277 |
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15.1 J.S. Mill and R.A. Fisher: Reducing Heterogeneity or Introducing Random Assignment |
277 |
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15.2 A Larger, More Heterogeneous Study Versus a Smaller, Less Heterogeneous Study |
279 |
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15.3 Heterogeneity and the Sensitivity of Point Estimates |
283 |
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15.4 Examples of Efforts to Reduce Heterogeneity |
284 |
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15.5 Summary |
286 |
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15.6 Further Reading |
286 |
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References |
286 |
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16 Uncommon but Dramatic Responses to Treatment |
288 |
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16.1 Large Effects, Now and Then |
288 |
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16.2 Two Examples |
291 |
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16.3 Properties of a Paired Version of Salsburg’s Model |
293 |
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16.4 Design Sensitivity for Uncommon but Dramatic Effects |
295 |
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16.5 Summary |
297 |
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16.6 Further Reading |
298 |
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16.7 Appendix: Sketch of the Proof of Proposition 16.1 |
298 |
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References |
299 |
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17 Anticipated Patterns of Response |
300 |
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17.1 Using Design Sensitivity to Evaluate Devices |
300 |
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17.2 Coherence |
300 |
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17.3 Doses |
304 |
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17.4 Example: Maimonides’ Rule |
309 |
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17.5 Further Reading |
310 |
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17.6 Appendix: Proof of Proposition 17.1 |
310 |
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References |
311 |
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Part IV: Planning Analysis |
313 |
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18 After Matching, Before Analysis |
314 |
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18.1 Split Samples and Design Sensitivity |
314 |
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18.2 Are Analytic Adjustments Feasible? |
316 |
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18.3 Matching and Thick Description |
321 |
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18.4 Further Reading |
323 |
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References |
323 |
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19 Planning the Analysis |
326 |
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19.1 Plans Enable |
326 |
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19.2 Elaborate Theories |
328 |
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19.3 Three Simple Plans with Two Control Groups |
329 |
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19.4 Sensitivity Analysis for Two Outcomes and Coherence |
338 |
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19.5 Sensitivity Analysis for Tests of Equivalence |
340 |
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19.6 Sensitivity Analysis for Equivalence and Difference |
342 |
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19.7 Summary |
344 |
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19.8 Further Reading |
344 |
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19.9 Appendix: Testing Hypotheses in Order |
345 |
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References |
349 |
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Summary: Key Elements of Design |
351 |
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Solutions to Common Problems |
353 |
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References |
356 |
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Symbols |
357 |
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Acronyms |
359 |
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Glossary of Statistical Terms |
361 |
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Some Books |
367 |
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References |
367 |
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Suggested Readings for a Course |
369 |
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References |
369 |
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Index |
371 |
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