What's the difference between algebra and arithmetic?

Algebra


Definition:

  • (n.) That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
  • (n.) A treatise on this science.

Example Sentences:

  • (1) Alphaxalone and endogenous steroid hormone metabolites inhibit the binding of [35S]-t-butyl bicyclophosphorothionate in some regions, enhance it in others and give biphasic concentration-dependence in others, apparently the result of algebraic summation of two effects involving regional-dependent enhancement or inhibition.
  • (2) When likelihood ratios are expressed as an algebraic function, maximum values are easily determined, hence fixing the limits of DNA analysis.
  • (3) Older subjects gave higher absolute error correction scores especially at the low error discriminability level, and the younger subjects did not show the negative correction bias (algebraic error) as suggested by the performance of the two older groups.
  • (4) Many tasks (e.g., solving algebraic equations and running errands) require the execution of several component processes in an unconstrained order.
  • (5) algebraic sum of these three cosine functions yielded a circadian waveform with peak-times occurring near 0300 and 1130 hr and a trough-time about 2200 hr.
  • (6) Parameters of quantitative genetic models have traditionally been estimated by either algebraic manipulation of familial correlations (or familial mean squares), biometric model fitting, or multiple-group covariance structure analysis.
  • (7) The slight diminution of this increase when (+)-erythro-DOPS was administered after inhibition of peripheral decarboxylase, might result from the algebraic sum of two inversely acting processes: suppression of NE synthesis in the capillary walls and enhancement of parenchymatous NE in some brain areas.
  • (8) The effect of self fertilization on the distribution of genetic types in a population can be represented algebraically by a linear transformation.
  • (9) Theories of denture retention have suffered from confusion of model, algebraic errors, and misapprehension of the physics of capillarity, adhesion and cohesion, as well as the role of atmospheric pressure.
  • (10) This derivation, stemming from first principles and founded on experimental data, does not quantitatively specify the additive (K'1) or multiplicative constant (K'2), but constrains the algebraic relationship of QT as a function of R-R.
  • (11) An algebraic analysis of patterns of hospitalization and case-control selection demonstrates that Berkson's bias will be avoided if both cases and controls are chosen from the community or if he = 0.
  • (12) By simple algebraic manipulation, Zelman introduced a pair of new reflection coefficients, and a third new parameter gamma which he misleadingly calls the "deviation from the dilute solution approximation."
  • (13) He merely wanted to highlight how Islam, which produced algebra and kept safe the Greek philosophers of antiquity in the middle ages, had lost its way scientifically by focusing too much on the study of religion.
  • (14) The graphic representation of family data for the computation of the coefficients of inbreeding [F] and relationship [r] can be replaced by an algebraic method.
  • (15) Traditional "stimulus-time-locked signal averaging" of human EEG, as usually practiced in both clinical and basic contexts, assumes the superposition principle of algebraic summation for a linear time series.
  • (16) Analysis of an algebraic model of multi-level exposure misclassification reveals that all odds ratios based on the misclassified data are constrained between the nonmisclassified odds ratio for the most extreme category and the inverse of this value.
  • (17) Then the integral equation is reduced to a system of algebraic equations of z - 1th degree with N + 1 unknowns.
  • (18) In the Appendix to this paper an algebraic relation is given which must be satisfied for two cysteine residues to make a disulfide bond.
  • (19) Understanding patterns that are associated with survival or death may require alternative mathematic approaches, such as group and set theory manipulated by principles of Boolean algebra.
  • (20) Concordance-dependent ascertainment is easily modeled algebraically; non-independent ascertainment is more complex and we here propose a model based on survival analysis.

Arithmetic


Definition:

  • (n.) The science of numbers; the art of computation by figures.
  • (n.) A book containing the principles of this science.

Example Sentences:

  • (1) Two different mental stressors were used: a mental arithmetic task with low stimulus intensity and one with high stimulus intensity characterised by more challenging instructions, a more competitive situation, and exposure to affective noise.
  • (2) From the patients' performance we make the following theoretical claims: that some arithmetic facts are stored in the form of individual fact representations (e.g., 9 x 4 = 36), whereas other facts are stored in the form of a general rule (e.g., 0 x N = 0); that arithmetic fact retrieval is mediated by abstract internal representations that are independent of the form in which problems are presented or responses are given; that arithmetic facts and calculation procedures are functionally independent; and that calculation algorithms may include special-case procedures that function to increase the speed or efficiency of problem solving.
  • (3) Staphylococcal phage types per milk sample ranged from 0 to 5, 0 to 7, and 0 to 8, with arithmetic means of 1.9, 2.3, and 2.3, respectively.
  • (4) This study compared changes in forearm blood flow, forearm vascular resistance, blood pressure, and heart rate elicited by mental stress (mental arithmetic) in 12 adolescents with a hypertensive parent and 13 age-matched adolescents with normotensive parents.
  • (5) The actual level of each variable observed during the arithmetic task was compared with the level predicted from the exercise by paired t-tests.
  • (6) One hundred isolates were tested in triplicate, and geometric mean MICs were plotted against arithmetic mean zone diameters and regression statistics calculated.
  • (7) The mean plasma values (arithmetic mean) of cadmium, lead, and mercury in industrial area were 0.53, 6.37, and 0.37 micrograms.100 ml-1 in maternal blood and 0.30, 4.82, and 0.31 micrograms.100 ml-1 in cord blood.
  • (8) Subjects were grouped, by using a median-split on their total mathematical performance scores, into a group of 10 low in arithmetic skill and a group of 10 high in arithmetic skill.
  • (9) In the 22 patients who performed 10-minute mental arithmetic, the changes persisted throughout mental exercise.
  • (10) The effect-addition model predicts that the combined action of two drugs is equal to the arithmetic sum of the individual effects.
  • (11) Neuropsychological complications occurred in conjunction with high urea levels in all patients, indicating varying degrees of impaired performance in motor tactile, receptive language, arithmetic, and intellectual functions.
  • (12) ADD boys with internalizing-type diagnoses had lower verbal IQs and arithmetic scores and performed more poorly on attention tasks than those without; parents also rated them more adversely.
  • (13) A greater degree of EEG desynchronization during mental arithmetic was found over the left hemisphere and the right occipital area.
  • (14) During work they were required to solve a constant flow of arithmetic problems, listen to music, or work in an unfilled control condition.
  • (15) Upon exiting the water, the divers did a series of arithmetic computations.
  • (16) When the distractor was an auditory arithmetic task, no difference emerged between the two hands for the retention of touches to the fingers; however, when the distractor was a tactual maze task executed by the right hand, asymmetry in favor of the left hand was observed.
  • (17) A placebo response was seen in just over half of the volunteers when the cardiovascular changes to mental arithmetic induced stress in healthy volunteers were measured.
  • (18) After the letter strings vanished from the screen the subjects were to press the space-bar whereby a mental arithmetic task was presented corresponding in difficulty to the preceding message.
  • (19) Since the arithmetic mean thickness of the tissue layers and of the air-blood barrier are the same in the two altitudinal groups, the average alveolus must have a smaller volume in the high-altitude mice.
  • (20) The effects of alcohol tolerance on stress sensitivity to venipuncture and mental arithmetics, on acute ethanol effects, and on ethanol-induced modifications of stress responses were tested in 44 healthy male volunteers selected according to a questionnaire as 22 high (HC) and low (LC) habitual consumers of alcohol each.